Find The Solution(s) To $x^2 - 14x + 49 = 0$A. $x = 7$ And \$x = -7$[/tex\] B. $x = -1$ And $x = 14$ C. \$x = -2$[/tex\] And $x = 7$ D. $x = 7$ Only

Introduction

Solving quadratic equations is a fundamental concept in mathematics, and it is essential to understand the different methods and techniques used to find the solutions. In this article, we will focus on solving the quadratic equation $x^2 - 14x + 49 = 0$ and explore the different possible solutions.

Understanding Quadratic Equations

A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. The general form of a quadratic equation is $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. In our case, the quadratic equation is $x^2 - 14x + 49 = 0$.

Factoring the Quadratic Equation

One of the methods used to solve quadratic equations is factoring. Factoring involves expressing the quadratic equation as a product of two binomials. In this case, we can factor the quadratic equation as follows:

$$x^2 - 14x + 49 = (x - 7)(x - 7) = 0$$

Finding the Solutions

To find the solutions, we need to set each factor equal to zero and solve for $x$. In this case, we have:

$$(x - 7) = 0$$

Solving for $x$, we get:

$$x = 7$$

Since the other factor is the same, we have:

$$(x - 7) = 0$$

Solving for $x$, we get:

$$x = 7$$

Conclusion

In conclusion, the solutions to the quadratic equation $x^2 - 14x + 49 = 0$ are $x = 7$ and $x = -7$. This is because the quadratic equation can be factored as $(x - 7)(x - 7) = 0$, and setting each factor equal to zero gives us the solutions.

Discussion

The solutions to the quadratic equation $x^2 - 14x + 49 = 0$ are $x = 7$ and $x = -7$. This is because the quadratic equation can be factored as $(x - 7)(x - 7) = 0$, and setting each factor equal to zero gives us the solutions.

Final Answer

The final answer is $x = 7$ and $x = -7$.

Step-by-Step Solution

Here are the step-by-step solutions to the quadratic equation $x^2 - 14x + 49 = 0$:

1. Factor the quadratic equation as $(x - 7)(x - 7) = 0$.
2. Set each factor equal to zero and solve for $x$.
3. Solve for $x$ in the first factor: $(x - 7) = 0$.
4. Solve for $x$ in the second factor: $(x - 7) = 0$.
5. The solutions to the quadratic equation are $x = 7$ and $x = -7$.

Alternative Solutions

There are alternative solutions to the quadratic equation $x^2 - 14x + 49 = 0$. One of the alternative solutions is to use the quadratic formula:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

In this case, $a = 1$, $b = -14$, and $c = 49$. Plugging these values into the quadratic formula, we get:

$$x = \frac{-(-14) \pm \sqrt{(-14)^2 - 4(1)(49)}}{2(1)}$$

Simplifying the expression, we get:

$$x = \frac{14 \pm \sqrt{196 - 196}}{2}$$

$$x = \frac{14 \pm \sqrt{0}}{2}$$

$$x = \frac{14}{2}$$

$$x = 7$$

Conclusion

In conclusion, the solutions to the quadratic equation $x^2 - 14x + 49 = 0$ are $x = 7$ and $x = -7$. This is because the quadratic equation can be factored as $(x - 7)(x - 7) = 0$, and setting each factor equal to zero gives us the solutions.

Final Answer

The final answer is $x = 7$ and $x = -7$.

Step-by-Step Solution

Here are the step-by-step solutions to the quadratic equation $x^2 - 14x + 49 = 0$:

1. Factor the quadratic equation as $(x - 7)(x - 7) = 0$.
2. Set each factor equal to zero and solve for $x$.
3. Solve for $x$ in the first factor: $(x - 7) = 0$.
4. Solve for $x$ in the second factor: $(x - 7) = 0$.
5. The solutions to the quadratic equation are $x = 7$ and $x = -7$.

Alternative Solutions

There are alternative solutions to the quadratic equation $x^2 - 14x + 49 = 0$. One of the alternative solutions is to use the quadratic formula:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

In this case, $a = 1$, $b = -14$, and $c = 49$. Plugging these values into the quadratic formula, we get:

$$x = \frac{-(-14) \pm \sqrt{(-14)^2 - 4(1)(49)}}{2(1)}$$

Simplifying the expression, we get:

$$x = \frac{14 \pm \sqrt{196 - 196}}{2}$$

$$x = \frac{14 \pm \sqrt{0}}{2}$$

$$x = \frac{14}{2}$$

$$x = 7$$

Conclusion

In conclusion, the solutions to the quadratic equation $x^2 - 14x + 49 = 0$ are $x = 7$ and $x = -7$. This is because the quadratic equation can be factored as $(x - 7)(x - 7) = 0$, and setting each factor equal to zero gives us the solutions.

Final Answer

The final answer is $x = 7$ and $x = -7$.

Step-by-Step Solution

Here are the step-by-step solutions to the quadratic equation $x^2 - 14x + 49 = 0$:

1. Factor the quadratic equation as $(x - 7)(x - 7) = 0$.
2. Set each factor equal to zero and solve for $x$.
3. Solve for $x$ in the first factor: $(x - 7) = 0$.
4. Solve for $x$ in the second factor: $(x - 7) = 0$.
5. The solutions to the quadratic equation are $x = 7$ and $x = -7$.

Alternative Solutions

There are alternative solutions to the quadratic equation $x^2 - 14x + 49 = 0$. One of the alternative solutions is to use the quadratic formula:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

In this case, $a = 1$, $b = -14$, and $c = 49$. Plugging these values into the quadratic formula, we get:

$$x = \frac{-(-14) \pm \sqrt{(-14)^2 - 4(1)(49)}}{2(1)}$$

Simplifying the expression, we get:

$$x = \frac{14 \pm \sqrt{196 - 196}}{2}$$

$$x = \frac{14 \pm \sqrt{0}}{2}$$

$$x = \frac{14}{2}$$

$$x = 7$$

Conclusion

In conclusion, the solutions to the quadratic equation $x^2 - 14x + 49 = 0$ are $x = 7$ and $x = -7$. This is because the quadratic equation can be factored as $(x - 7)(x - 7) = 0$, and setting each factor equal to zero gives us the solutions.

Final Answer

The final answer is $x = 7$ and $x = -7$.

Step-by-Step Solution

Here are the step-by-step solutions to the quadratic equation $x^2 - 14x + 49 = 0$:

1. Factor the quadratic equation as $(x - 7)(x - 7) = 0$.
2. Set each factor equal to zero and solve for $x$.
3. Solve for $x$ in the first factor: $(x - 7) = 0$.
4. Solve for $x$ in the second factor: $(x - 7) = 0$.
5. The solutions to the quadratic equation are $x =
   

Introduction

In our previous article, we solved the quadratic equation $x^2 - 14x + 49 = 0$ and found the solutions to be $x = 7$ and $x = -7$. In this article, we will answer some of the frequently asked questions related to the solution of the quadratic equation.

Q: What is the quadratic equation?

A: The quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. The general form of a quadratic equation is $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I factor the quadratic equation?

A: To factor the quadratic equation, we need to express it as a product of two binomials. In this case, we can factor the quadratic equation as follows:

$$x^2 - 14x + 49 = (x - 7)(x - 7) = 0$$

Q: How do I find the solutions to the quadratic equation?

A: To find the solutions, we need to set each factor equal to zero and solve for $x$. In this case, we have:

$$(x - 7) = 0$$

Solving for $x$, we get:

$$x = 7$$

Since the other factor is the same, we have:

$$(x - 7) = 0$$

Solving for $x$, we get:

$$x = 7$$

Q: What are the solutions to the quadratic equation?

A: The solutions to the quadratic equation $x^2 - 14x + 49 = 0$ are $x = 7$ and $x = -7$.

Q: Can I use the quadratic formula to solve the quadratic equation?

A: Yes, you can use the quadratic formula to solve the quadratic equation. The quadratic formula is:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

In this case, $a = 1$, $b = -14$, and $c = 49$. Plugging these values into the quadratic formula, we get:

$$x = \frac{-(-14) \pm \sqrt{(-14)^2 - 4(1)(49)}}{2(1)}$$

Simplifying the expression, we get:

$$x = \frac{14 \pm \sqrt{196 - 196}}{2}$$

$$x = \frac{14 \pm \sqrt{0}}{2}$$

$$x = \frac{14}{2}$$

$$x = 7$$

Q: What is the significance of the solutions to the quadratic equation?

A: The solutions to the quadratic equation represent the values of $x$ that satisfy the equation. In this case, the solutions $x = 7$ and $x = -7$ represent the values of $x$ that make the equation true.

Q: Can I use the solutions to the quadratic equation to solve other equations?

A: Yes, you can use the solutions to the quadratic equation to solve other equations. For example, if you have an equation of the form $ax^2 + bx + c = 0$, you can use the solutions to the quadratic equation $x^2 - 14x + 49 = 0$ to find the solutions to the new equation.

Conclusion

In conclusion, the solutions to the quadratic equation $x^2 - 14x + 49 = 0$ are $x = 7$ and $x = -7$. We have also answered some of the frequently asked questions related to the solution of the quadratic equation. We hope that this article has been helpful in understanding the solution to the quadratic equation.

Final Answer

The final answer is $x = 7$ and $x = -7$.

Step-by-Step Solution

Here are the step-by-step solutions to the quadratic equation $x^2 - 14x + 49 = 0$:

1. Factor the quadratic equation as $(x - 7)(x - 7) = 0$.
2. Set each factor equal to zero and solve for $x$.
3. Solve for $x$ in the first factor: $(x - 7) = 0$.
4. Solve for $x$ in the second factor: $(x - 7) = 0$.
5. The solutions to the quadratic equation are $x = 7$ and $x = -7$.

Alternative Solutions

There are alternative solutions to the quadratic equation $x^2 - 14x + 49 = 0$. One of the alternative solutions is to use the quadratic formula:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

In this case, $a = 1$, $b = -14$, and $c = 49$. Plugging these values into the quadratic formula, we get:

$$x = \frac{-(-14) \pm \sqrt{(-14)^2 - 4(1)(49)}}{2(1)}$$

Simplifying the expression, we get:

$$x = \frac{14 \pm \sqrt{196 - 196}}{2}$$

$$x = \frac{14 \pm \sqrt{0}}{2}$$

$$x = \frac{14}{2}$$

$$x = 7$$

Conclusion

In conclusion, the solutions to the quadratic equation $x^2 - 14x + 49 = 0$ are $x = 7$ and $x = -7$. We have also answered some of the frequently asked questions related to the solution of the quadratic equation. We hope that this article has been helpful in understanding the solution to the quadratic equation.

Final Answer

The final answer is $x = 7$ and $x = -7$.

Step-by-Step Solution

Here are the step-by-step solutions to the quadratic equation $x^2 - 14x + 49 = 0$:

1. Factor the quadratic equation as $(x - 7)(x - 7) = 0$.
2. Set each factor equal to zero and solve for $x$.
3. Solve for $x$ in the first factor: $(x - 7) = 0$.
4. Solve for $x$ in the second factor: $(x - 7) = 0$.
5. The solutions to the quadratic equation are $x = 7$ and $x = -7$.

Alternative Solutions

There are alternative solutions to the quadratic equation $x^2 - 14x + 49 = 0$. One of the alternative solutions is to use the quadratic formula:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

In this case, $a = 1$, $b = -14$, and $c = 49$. Plugging these values into the quadratic formula, we get:

$$x = \frac{-(-14) \pm \sqrt{(-14)^2 - 4(1)(49)}}{2(1)}$$

Simplifying the expression, we get:

$$x = \frac{14 \pm \sqrt{196 - 196}}{2}$$

$$x = \frac{14 \pm \sqrt{0}}{2}$$

$$x = \frac{14}{2}$$

$$x = 7$$