X^2+y^2=(X+y)

Solution for X^2+y^2=(X+y) equation:

X^2+X^2=(X+X)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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


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

(+2X)

We get rid of parentheses

2X

Back to the equation:

-(2X)


a = 2; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·2·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*2}=\frac{0}{4}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*2}=\frac{4}{4}
=1
$