Solve the following equation. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (x+ 12)2 = 14 O A. The solution(s) is(are) x= (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) B. There are no real solutions.
Solve the following equation. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (x+ 12)2 = 14 O A. The solution(s) is(are) x= (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) B. There are no real solutions.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.5: Solving Quadratic Equations By Completing The Square
Problem 41PPS
Related questions
Question
![### Solving the Quadratic Equation
#### Problem Statement:
Solve the following equation:
\[
(x + 12)^2 = 14
\]
#### Instructions:
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
#### Answer Choices:
- **A.** The solution(s) is (are) \( x = \) _________
*(Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)*
- **B.** There are no real solutions.
#### Explanation:
This problem presents a quadratic equation in the form \((x + 12)^2 = 14\). To solve for \(x\), follow these steps:
1. **Expand the Equation:**
\[
(x + 12)^2 = 14
\]
Take the square root of both sides:
\[
x + 12 = \pm \sqrt{14}
\]
2. **Isolate \(x\):**
\[
x = -12 \pm \sqrt{14}
\]
Therefore, the solutions will be:
\[
x = -12 + \sqrt{14}, \, -12 - \sqrt{14}
\]
Use the provided answer box in choice A to input the solutions using the exact values as shown above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb48b187-83f1-4dc9-80dd-ddef9eb815af%2Fa332c04e-5ba9-4b28-ad46-8ead1855f5b1%2Fsuytdp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving the Quadratic Equation
#### Problem Statement:
Solve the following equation:
\[
(x + 12)^2 = 14
\]
#### Instructions:
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
#### Answer Choices:
- **A.** The solution(s) is (are) \( x = \) _________
*(Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)*
- **B.** There are no real solutions.
#### Explanation:
This problem presents a quadratic equation in the form \((x + 12)^2 = 14\). To solve for \(x\), follow these steps:
1. **Expand the Equation:**
\[
(x + 12)^2 = 14
\]
Take the square root of both sides:
\[
x + 12 = \pm \sqrt{14}
\]
2. **Isolate \(x\):**
\[
x = -12 \pm \sqrt{14}
\]
Therefore, the solutions will be:
\[
x = -12 + \sqrt{14}, \, -12 - \sqrt{14}
\]
Use the provided answer box in choice A to input the solutions using the exact values as shown above.
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