x2+(x+5)2=233

Solution for x2+(x+5)2=233 equation:

x2+(x+5)2=233

We move all terms to the left:

x2+(x+5)2-(233)=0

We add all the numbers together, and all the variables

x^2+(x+5)2-233=0

We multiply parentheses

x^2+2x+10-233=0

We add all the numbers together, and all the variables

x^2+2x-223=0

a = 1; b = 2; c = -223;
Δ = b2-4ac
Δ = 22-4·1·(-223)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8\sqrt{14}}{2*1}=\frac{-2-8\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8\sqrt{14}}{2*1}=\frac{-2+8\sqrt{14}}{2}
$