7^2+x^2=312

Solution for 7^2+x^2=312 equation:

7^2+x^2=312

We move all terms to the left:

7^2+x^2-(312)=0

determiningTheFunctionDomain
x^2-312+7^2=0

We add all the numbers together, and all the variables

x^2-263=0

a = 1; b = 0; c = -263;
Δ = b2-4ac
Δ = 02-4·1·(-263)
Δ = 1052
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:

$\sqrt{\Delta}=\sqrt{1052}=\sqrt{4*263}=\sqrt{4}*\sqrt{263}=2\sqrt{263}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{263}}{2*1}=\frac{0-2\sqrt{263}}{2}
=-\frac{2\sqrt{263}}{2}
=-\sqrt{263}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{263}}{2*1}=\frac{0+2\sqrt{263}}{2}
=\frac{2\sqrt{263}}{2}
=\sqrt{263}
$