Use the property below to help solve the quadratic equation.

Question

Use the property below to help solve the quadratic equation. (Enter your answers as a comma-separated list.)
For any real number a, x² = a if and only if x = √a or x = −√a

2(x + 4)² − 7 = 25

 

x =

Answer 1

2(x+4)²-7=25

2(x+4)²=25+7

2(x+4)²=32

(x+4)²=32/2

(x+4)²=16

(x+4)=√16 or (x+4)=-√16

x+4=4 or x+4=-4

x=0 or x=-8

Answer 2

We are in the position to easily solve this equation without the use of the quadratic formula.

 

 

Add 7 on both sides of equation.

 

2(x + 4)² = 32

 

 

Divide both sides of equation by 2.

 

(x + 4)² = 16

 

 

Square-root both sides of equation to undo the exponent.

 

x + 4 = ±√(16)

 

 

Subtract 4 on both sides of equation.

 

x = -4 ± √(16)

 

x = -4 + √(16)           and         x = -4 - √(16)

 

x = -4 + 4                  and         x = -4 - 4

 

x = 0                       and             x = -8

 

 

In the end, we have two solutions since we have a positive and negative sign in front of the square-root.