x2+8x+16=(x+4)2

Solution for x2+8x+16=(x+4)2 equation:

x2+8x+16=(x+4)2

We move all terms to the left:

x2+8x+16-((x+4)2)=0

We add all the numbers together, and all the variables

x^2+8x-((x+4)2)+16=0


We calculate terms in parentheses: -((x+4)2), so:

(x+4)2

We multiply parentheses

2x+8

Back to the equation:

-(2x+8)


We get rid of parentheses

x^2+8x-2x-8+16=0

We add all the numbers together, and all the variables

x^2+6x+8=0

a = 1; b = 6; c = +8;
Δ = b2-4ac
Δ = 62-4·1·8
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2}{2*1}=\frac{-4}{2}
=-2
$