(5*5)+(6*6)=(x*x)

Solution for (5*5)+(6*6)=(x*x) equation:

(5*5)+(6*6)=(x*x)

We move all terms to the left:

(5*5)+(6*6)-((x*x))=0

We add all the numbers together, and all the variables

-((+x*x))+25+36=0

We add all the numbers together, and all the variables

-((+x*x))+61=0


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

(+x*x)

We get rid of parentheses

x*x

Wy multiply elements

x^2

Back to the equation:

-(x^2)


We add all the numbers together, and all the variables

-1x^2+61=0

a = -1; b = 0; c = +61;
Δ = b2-4ac
Δ = 02-4·(-1)·61
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{61}}{2*-1}=\frac{0-2\sqrt{61}}{-2}
=-\frac{2\sqrt{61}}{-2}
=-\frac{\sqrt{61}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{61}}{2*-1}=\frac{0+2\sqrt{61}}{-2}
=\frac{2\sqrt{61}}{-2}
=\frac{\sqrt{61}}{-1}
$