(6)^2+(x)^2=(25)^2

Solution for (6)^2+(x)^2=(25)^2 equation:

(6)^2+(x)^2=(25)^2

We move all terms to the left:

(6)^2+(x)^2-((25)^2)=0

determiningTheFunctionDomain
x^2+6^2-25^2=0

We add all the numbers together, and all the variables

x^2-589=0

a = 1; b = 0; c = -589;
Δ = b2-4ac
Δ = 02-4·1·(-589)
Δ = 2356
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:

$\sqrt{\Delta}=\sqrt{2356}=\sqrt{4*589}=\sqrt{4}*\sqrt{589}=2\sqrt{589}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{589}}{2*1}=\frac{0-2\sqrt{589}}{2}
=-\frac{2\sqrt{589}}{2}
=-\sqrt{589}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{589}}{2*1}=\frac{0+2\sqrt{589}}{2}
=\frac{2\sqrt{589}}{2}
=\sqrt{589}
$