Question

Solve for x. Enter the solutions from least to greatest.
(x + 7)^2 - 49 = 0

Answer 1

Lesser x=-14 Greater x=0

Explanation:

x+7)

2

−49

(x+7)

2

(x+7)

2

​

​

=0

=49

=

49

​

​

Hint #22 / 3

\begin{aligned} x+7&=\pm7 \\\\ x&=\pm7-7 \\ \phantom{(x + 7)^2 - 49}& \\ x=-14&\text{ or }x=0 \end{aligned}

x+7

x

(x+7)

2

−49

x=−14

​

=±7

=±7−7

or x=0

​

Answer 2

x = -14, 0

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS
• Equality Properties

Algebra I

• Completing the Square
• Multiple Roots/Solutions

Explanation:

Step 1: Define

(x + 7)² - 49 = 0

Step 2: Solve for x

1. Add 49 to both sides: (x + 7)² = 49
2. Square root both sides: x + 7 = ±7
3. Subtract 7 on both sides: x = -7 ± 7
4. Evaluate: x = -14, 0

Step 3: Check

Plug in x values into original equation to verify they are a solution.

x = -14

1. Substitute in x: (-14 + 7)² - 49 = 0
2. Add: (-7)² - 49 = 0
3. Exponents: 49 - 49 = 0
4. Subtract: 0 = 0

Here we see that 0 does indeed equal 0.

∴ x = -14 is a solution of the equation

x = 0

1. Substitute in x: (0 + 7)² - 49 = 0
2. Add: 7² - 49 = 0
3. Exponents: 49 - 49 = 0
4. Subtract: 0 = 0

Here we see that 0 does indeed equal 0.

∴ x = 0 is also a solution of the equation.