Solve the quadratic equation by using the square root property. Enter the exact answers. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or x + 1; x-1). The order of the list does not matter. To enter a, type sqrt(a). (x-7)² = 4 x=
Solve the quadratic equation by using the square root property. Enter the exact answers. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or x + 1; x-1). The order of the list does not matter. To enter a, type sqrt(a). (x-7)² = 4 x=
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Solving Quadratic Equations Using the Square Root Property**
To solve the quadratic equation using the square root property, consider the following:
\[
(x - 7)^2 = 4
\]
**Steps:**
1. **Recognize the Form:**
The equation is in the standard form \((x - a)^2 = b\).
2. **Apply the Square Root Property:**
To solve, take the square root of both sides:
\[
x - 7 = \pm \sqrt{4}
\]
3. **Solve for x:**
\[
x - 7 = 2 \quad \text{or} \quad x - 7 = -2
\]
4. **Find Exact Answers:**
- \(x = 9\)
- \(x = 5\)
The field below allows the input of numbers or formulas separated by semicolons, such as:
\(2; 4; 6\) or \(x + 1; x - 1\). The order does not matter.
**Note:** To enter a square root like \(\sqrt{a}\), type `sqrt(a)`.
**Input Box:**
\[
x = \_\_\_\_
\]
Use this format to submit your answers correctly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0caa6687-4e6f-4c6c-bc0f-3d83b65e20e1%2Fd1b0eae9-5ccc-437a-b035-f56f31e4f715%2Feyiz8ad_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solving Quadratic Equations Using the Square Root Property**
To solve the quadratic equation using the square root property, consider the following:
\[
(x - 7)^2 = 4
\]
**Steps:**
1. **Recognize the Form:**
The equation is in the standard form \((x - a)^2 = b\).
2. **Apply the Square Root Property:**
To solve, take the square root of both sides:
\[
x - 7 = \pm \sqrt{4}
\]
3. **Solve for x:**
\[
x - 7 = 2 \quad \text{or} \quad x - 7 = -2
\]
4. **Find Exact Answers:**
- \(x = 9\)
- \(x = 5\)
The field below allows the input of numbers or formulas separated by semicolons, such as:
\(2; 4; 6\) or \(x + 1; x - 1\). The order does not matter.
**Note:** To enter a square root like \(\sqrt{a}\), type `sqrt(a)`.
**Input Box:**
\[
x = \_\_\_\_
\]
Use this format to submit your answers correctly.
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