7^2+b^2=256

Solution for 7^2+b^2=256 equation:

7^2+b^2=256

We move all terms to the left:

7^2+b^2-(256)=0

determiningTheFunctionDomain
b^2-256+7^2=0

We add all the numbers together, and all the variables

b^2-207=0

a = 1; b = 0; c = -207;
Δ = b2-4ac
Δ = 02-4·1·(-207)
Δ = 828
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{23}}{2*1}=\frac{0-6\sqrt{23}}{2}
=-\frac{6\sqrt{23}}{2}
=-3\sqrt{23}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{23}}{2*1}=\frac{0+6\sqrt{23}}{2}
=\frac{6\sqrt{23}}{2}
=3\sqrt{23}
$