52=x2+(x+1)2

Solution for 52=x2+(x+1)2 equation:

52=x2+(x+1)2

We move all terms to the left:

52-(x2+(x+1)2)=0


We calculate terms in parentheses: -(x2+(x+1)2), so:

x2+(x+1)2

We add all the numbers together, and all the variables

x^2+(x+1)2

We multiply parentheses

x^2+2x+2

Back to the equation:

-(x^2+2x+2)


We get rid of parentheses

-x^2-2x-2+52=0

We add all the numbers together, and all the variables

-1x^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}
$