What Are The Solutions Of The Equation $(x+2)^2-2(x+2)-15=0$? Use $u$ Substitution To Solve.A. X = − 7 X=-7 X = − 7 And X = 1 X=1 X = 1 B. X = − 5 X=-5 X = − 5 And X = 3 X=3 X = 3 C. X = − 3 X=-3 X = − 3 And X = 5 X=5 X = 5 D. X = − 1 X=-1 X = − 1 And

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Introduction

Solving quadratic equations can be a challenging task, especially when they are not in the standard form. In this article, we will use the $u$ substitution method to solve the equation $(x+2)^2-2(x+2)-15=0$. This method involves substituting a variable, in this case, $u$, to simplify the equation and make it easier to solve.

Step 1: Substitute $u$ into the equation

To use the $u$ substitution method, we need to substitute $u$ into the equation. Let's substitute $u = x + 2$ into the equation.

(x+2)2−2(x+2)−15=0(x+2)^2-2(x+2)-15=0

u2−2u−15=0u^2 - 2u - 15 = 0

Step 2: Solve the quadratic equation

Now that we have the equation in the standard form, we can solve it using the quadratic formula or factoring. In this case, we can factor the equation.

u2−2u−15=0u^2 - 2u - 15 = 0

(u−5)(u+3)=0(u - 5)(u + 3) = 0

Step 3: Find the values of $u$

To find the values of $u$, we need to set each factor equal to zero and solve for $u$.

(u−5)=0(u - 5) = 0

u=5u = 5

(u+3)=0(u + 3) = 0

u=−3u = -3

Step 4: Find the values of $x$

Now that we have the values of $u$, we can find the values of $x$ by substituting $u = x + 2$ back into the equation.

u=5u = 5

x+2=5x + 2 = 5

x=3x = 3

u=−3u = -3

x+2=−3x + 2 = -3

x=−5x = -5

Conclusion

In this article, we used the $u$ substitution method to solve the equation $(x+2)^2-2(x+2)-15=0$. We substituted $u = x + 2$ into the equation, solved the quadratic equation, found the values of $u$, and finally found the values of $x$. The solutions to the equation are $x = -5$ and $x = 3$.

Final Answer

The final answer is: B\boxed{B}

Introduction

In our previous article, we used the $u$ substitution method to solve the equation $(x+2)^2-2(x+2)-15=0$. In this article, we will answer some frequently asked questions about solving this equation using the $u$ substitution method.

Q: What is the $u$ substitution method?

A: The $u$ substitution method is a technique used to solve quadratic equations by substituting a variable, in this case, $u$, to simplify the equation and make it easier to solve.

Q: Why do we need to use the $u$ substitution method?

A: We need to use the $u$ substitution method to simplify the equation and make it easier to solve. The equation $(x+2)^2-2(x+2)-15=0$ is not in the standard form, and the $u$ substitution method helps us to rewrite it in the standard form.

Q: How do we substitute $u$ into the equation?

A: To substitute $u$ into the equation, we need to replace $x + 2$ with $u$. So, the equation $(x+2)^2-2(x+2)-15=0$ becomes $u^2 - 2u - 15 = 0$.

Q: How do we solve the quadratic equation?

A: We can solve the quadratic equation using the quadratic formula or factoring. In this case, we can factor the equation $u^2 - 2u - 15 = 0$ to get $(u - 5)(u + 3) = 0$.

Q: How do we find the values of $u$?

A: To find the values of $u$, we need to set each factor equal to zero and solve for $u$. So, we get $u = 5$ and $u = -3$.

Q: How do we find the values of $x$?

A: To find the values of $x$, we need to substitute $u = x + 2$ back into the equation. So, we get $x = 3$ and $x = -5$.

Q: What are the solutions to the equation?

A: The solutions to the equation $(x+2)^2-2(x+2)-15=0$ are $x = -5$ and $x = 3$.

Q: Can we use the $u$ substitution method to solve any quadratic equation?

A: Yes, we can use the $u$ substitution method to solve any quadratic equation. However, we need to make sure that the equation is in the correct form and that we can substitute $u$ into the equation.

Q: What are the advantages of using the $u$ substitution method?

A: The advantages of using the $u$ substitution method are that it helps us to simplify the equation and make it easier to solve. It also helps us to avoid complex calculations and to find the solutions more easily.

Q: What are the disadvantages of using the $u$ substitution method?

A: The disadvantages of using the $u$ substitution method are that it can be time-consuming and that it requires a good understanding of algebraic manipulations.

Conclusion

In this article, we answered some frequently asked questions about solving the equation $(x+2)^2-2(x+2)-15=0$ using the $u$ substitution method. We hope that this article has helped you to understand the $u$ substitution method and to solve quadratic equations more easily.

Final Answer

The final answer is: B\boxed{B}