X2+(22-x)2=250

Solution for X2+(22-x)2=250 equation:

X2+(22-X)2=250

We move all terms to the left:

X2+(22-X)2-(250)=0

We add all the numbers together, and all the variables

X2+(-1X+22)2-250=0

We add all the numbers together, and all the variables

X^2+(-1X+22)2-250=0

We multiply parentheses

X^2-2X+44-250=0

We add all the numbers together, and all the variables

X^2-2X-206=0

a = 1; b = -2; c = -206;
Δ = b2-4ac
Δ = -22-4·1·(-206)
Δ = 828
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:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{23}}{2*1}=\frac{2-6\sqrt{23}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{23}}{2*1}=\frac{2+6\sqrt{23}}{2}
$