(x+5)(x+5)=199

Solution for (x+5)(x+5)=199 equation:

(x+5)(x+5)=199

We move all terms to the left:

(x+5)(x+5)-(199)=0

We multiply parentheses ..

(+x^2+5x+5x+25)-199=0

We get rid of parentheses

x^2+5x+5x+25-199=0

We add all the numbers together, and all the variables

x^2+10x-174=0

a = 1; b = 10; c = -174;
Δ = b2-4ac
Δ = 102-4·1·(-174)
Δ = 796
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{796}=\sqrt{4*199}=\sqrt{4}*\sqrt{199}=2\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{199}}{2*1}=\frac{-10-2\sqrt{199}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{199}}{2*1}=\frac{-10+2\sqrt{199}}{2}
$