Respuesta :

Space

Answer:

x = -14, 0

General Formulas and Concepts:

Pre-Algebra

  • Order of Operations: BPEMDAS
  • Equality Properties

Algebra I

  • Completing the Square
  • Multiple Roots/Solutions

Step-by-step 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.

mikaela4life051

Answer:

Lesser x=-14 Greater x=0

Step-by-step 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

​  

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