5^2=(x^2-11)

Solution for 5^2=(x^2-11) equation:

5^2=(x^2-11)

We move all terms to the left:

5^2-((x^2-11))=0

We add all the numbers together, and all the variables

-((x^2-11))+25=0


We calculate terms in parentheses: -((x^2-11)), so:

(x^2-11)

We get rid of parentheses

x^2-11

Back to the equation:

-(x^2-11)


We get rid of parentheses

-x^2+11+25=0

We add all the numbers together, and all the variables

-1x^2+36=0

a = -1; b = 0; c = +36;
Δ = b2-4ac
Δ = 02-4·(-1)·36
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*-1}=\frac{-12}{-2}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-1}=\frac{12}{-2}
=-6
$