X2+(x+2)2=52

Solution for X2+(x+2)2=52 equation:

X2+(X+2)2=52

We move all terms to the left:

X2+(X+2)2-(52)=0

We add all the numbers together, and all the variables

X^2+(X+2)2-52=0

We multiply parentheses

X^2+2X+4-52=0

We add all the numbers together, and all the variables

X^2+2X-48=0

a = 1; b = 2; c = -48;
Δ = b2-4ac
Δ = 22-4·1·(-48)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*1}=\frac{-16}{2}
=-8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*1}=\frac{12}{2}
=6
$