x2+x2=(x+10)2

Solution for x2+x2=(x+10)2 equation:

x2+x2=(x+10)2

We move all terms to the left:

x2+x2-((x+10)2)=0

We add all the numbers together, and all the variables

2x^2-((x+10)2)=0


We calculate terms in parentheses: -((x+10)2), so:

(x+10)2

We multiply parentheses

2x+20

Back to the equation:

-(2x+20)


We get rid of parentheses

2x^2-2x-20=0

a = 2; b = -2; c = -20;
Δ = b2-4ac
Δ = -22-4·2·(-20)
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{41}}{2*2}=\frac{2-2\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{41}}{2*2}=\frac{2+2\sqrt{41}}{4}
$