Answer: x=-9
Step-by-step explanation:
Expand the square; (x+4)^2=25; (x+4)(x+4)=25
Distribute;(x+4)(x+4)=25
x(x+4)+4(x+4)=25
Distribute;
x(x+4)+4(x+4)=25
x^2 + 4x +4(x+4)=25
Distribute;
x(x+4)+4(x+4)=25
x^2+4x+4x + 16=25
Combine like terms;
x^2+4x+4x + 16=25
x^2+8x+16=25
Move the terms to left
x^2+8x+16=25
x^2 + 8x + 16 - 25 =0
Subtract numbers
x^2 + 8x + 16 - 25 =0
x^2 +8x-9=0
Identify a, b, and c in your equation and then find two numbers that when multiplied together equal c and when added together equal b.
x^2 +8x-9=0
Write your equation in factored form
(x-1)(x+9)=0
Set each factor equal to zero
x-1=0
x+9=0
Rearrange and isolate the variable to find each solution
x = 1
x = -9