X2+(x+7)2=172

Solution for X2+(x+7)2=172 equation:

X2+(X+7)2=172

We move all terms to the left:

X2+(X+7)2-(172)=0

We add all the numbers together, and all the variables

X^2+(X+7)2-172=0

We multiply parentheses

X^2+2X+14-172=0

We add all the numbers together, and all the variables

X^2+2X-158=0

a = 1; b = 2; c = -158;
Δ = b2-4ac
Δ = 22-4·1·(-158)
Δ = 636
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:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{159}}{2*1}=\frac{-2-2\sqrt{159}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{159}}{2*1}=\frac{-2+2\sqrt{159}}{2}
$