X2+(12-x)2=74

Solution for X2+(12-x)2=74 equation:

X2+(12-X)2=74

We move all terms to the left:

X2+(12-X)2-(74)=0

We add all the numbers together, and all the variables

X2+(-1X+12)2-74=0

We add all the numbers together, and all the variables

X^2+(-1X+12)2-74=0

We multiply parentheses

X^2-2X+24-74=0

We add all the numbers together, and all the variables

X^2-2X-50=0

a = 1; b = -2; c = -50;
Δ = b2-4ac
Δ = -22-4·1·(-50)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{51}}{2*1}=\frac{2-2\sqrt{51}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{51}}{2*1}=\frac{2+2\sqrt{51}}{2}
$