Solve The Equation. Check Your Solutions. Write Your Solutions From Least To Greatest, Separated By A Comma If Necessary.${ \begin{array}{l} (k+1)^2 = 9 \ k = \square, \square \end{array} }$

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Introduction

In this article, we will be solving a quadratic equation and checking our solutions. The equation given is (k+1)2=9(k+1)^2 = 9, and we need to find the values of kk that satisfy this equation. We will then check our solutions to ensure they are correct and write them from least to greatest, separated by commas if necessary.

Step 1: Expand the Equation

The first step in solving this equation is to expand the left-hand side. We can do this by using the formula (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2. In this case, a=k+1a = k+1 and b=0b = 0, so we have:

(k+1)2=(k+1)(k+1)=k2+2k+1(k+1)^2 = (k+1)(k+1) = k^2 + 2k + 1

Step 2: Set Up the Equation

Now that we have expanded the left-hand side, we can set up the equation by equating it to the right-hand side:

k2+2k+1=9k^2 + 2k + 1 = 9

Step 3: Rearrange the Equation

To make it easier to solve, we can rearrange the equation by subtracting 9 from both sides:

k2+2k−8=0k^2 + 2k - 8 = 0

Step 4: Factor the Equation

This quadratic equation can be factored as:

(k+4)(k−2)=0(k+4)(k-2) = 0

Step 5: Solve for kk

To find the values of kk, we can set each factor equal to zero and solve for kk:

k+4=0⇒k=−4k+4 = 0 \Rightarrow k = -4

k−2=0⇒k=2k-2 = 0 \Rightarrow k = 2

Step 6: Check the Solutions

To check our solutions, we can plug them back into the original equation:

(k+1)2=9(k+1)^2 = 9

For k=−4k = -4, we have:

(−4+1)2=(−3)2=9( -4 + 1)^2 = (-3)^2 = 9

This is true, so k=−4k = -4 is a valid solution.

For k=2k = 2, we have:

(2+1)2=(3)2=9( 2 + 1)^2 = (3)^2 = 9

This is also true, so k=2k = 2 is a valid solution.

Step 7: Write the Solutions

Now that we have checked our solutions, we can write them from least to greatest, separated by commas if necessary:

k=−4,2k = -4, 2

Conclusion

In this article, we solved a quadratic equation and checked our solutions. We found that the values of kk that satisfy the equation are −4-4 and 22. We then wrote these solutions from least to greatest, separated by commas if necessary.

Frequently Asked Questions

Q: What is the equation given in this article?

A: The equation given is (k+1)2=9(k+1)^2 = 9.

Q: What are the values of kk that satisfy the equation?

A: The values of kk that satisfy the equation are −4-4 and 22.

Q: How do you check the solutions?

A: To check the solutions, you can plug them back into the original equation.

Q: What is the final answer?

A: The final answer is k=−4,2k = -4, 2.

Additional Resources

For more information on solving quadratic equations, you can check out the following resources:

Related Articles

Glossary

  • Quadratic Equation: An equation of the form ax2+bx+c=0ax^2 + bx + c = 0, where aa, bb, and cc are constants.
  • Solution: A value that satisfies an equation.
  • Factor: A way of expressing an expression as a product of two or more expressions.
  • Rearrange: To change the order of the terms in an equation.
  • Check: To verify that a solution is correct.

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Introduction

In our previous article, we solved a quadratic equation and checked our solutions. We found that the values of kk that satisfy the equation are −4-4 and 22. In this article, we will answer some frequently asked questions about solving quadratic equations and checking solutions.

Q&A

Q: What is the equation given in this article?

A: The equation given is (k+1)2=9(k+1)^2 = 9.

Q: What are the values of kk that satisfy the equation?

A: The values of kk that satisfy the equation are −4-4 and 22.

Q: How do you check the solutions?

A: To check the solutions, you can plug them back into the original equation.

Q: What is the final answer?

A: The final answer is k=−4,2k = -4, 2.

Q: Can you explain the steps to solve the equation?

A: Yes, the steps to solve the equation are:

  1. Expand the left-hand side of the equation.
  2. Set up the equation by equating it to the right-hand side.
  3. Rearrange the equation by subtracting 9 from both sides.
  4. Factor the equation.
  5. Solve for kk by setting each factor equal to zero.
  6. Check the solutions by plugging them back into the original equation.

Q: What is the difference between a quadratic equation and a linear equation?

A: A quadratic equation is an equation of the form ax2+bx+c=0ax^2 + bx + c = 0, where aa, bb, and cc are constants. A linear equation is an equation of the form ax+b=0ax + b = 0, where aa and bb are constants.

Q: Can you explain the concept of factoring?

A: Factoring is a way of expressing an expression as a product of two or more expressions. For example, the expression x2+5x+6x^2 + 5x + 6 can be factored as (x+3)(x+2)(x+3)(x+2).

Q: How do you know if a solution is correct?

A: To check if a solution is correct, you can plug it back into the original equation. If the equation is true, then the solution is correct.

Q: Can you provide more examples of quadratic equations?

A: Yes, here are a few examples of quadratic equations:

  • x2+4x+4=0x^2 + 4x + 4 = 0
  • x2−6x+9=0x^2 - 6x + 9 = 0
  • x2+2x−15=0x^2 + 2x - 15 = 0

Q: Can you explain the concept of the quadratic formula?

A: The quadratic formula is a formula that can be used to solve quadratic equations. It is given by:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

This formula can be used to find the solutions to a quadratic equation.

Conclusion

In this article, we answered some frequently asked questions about solving quadratic equations and checking solutions. We hope that this article has been helpful in clarifying any confusion you may have had about these topics.

Frequently Asked Questions

Q: What is the equation given in this article?

A: The equation given is (k+1)2=9(k+1)^2 = 9.

Q: What are the values of kk that satisfy the equation?

A: The values of kk that satisfy the equation are −4-4 and 22.

Q: How do you check the solutions?

A: To check the solutions, you can plug them back into the original equation.

Q: What is the final answer?

A: The final answer is k=−4,2k = -4, 2.

Additional Resources

For more information on solving quadratic equations, you can check out the following resources:

Related Articles

Glossary

  • Quadratic Equation: An equation of the form ax2+bx+c=0ax^2 + bx + c = 0, where aa, bb, and cc are constants.
  • Solution: A value that satisfies an equation.
  • Factor: A way of expressing an expression as a product of two or more expressions.
  • Rearrange: To change the order of the terms in an equation.
  • Check: To verify that a solution is correct.