(5*5)+(h*h)=64

Solution for (5*5)+(h*h)=64 equation:

(5*5)+(h*h)=64

We move all terms to the left:

(5*5)+(h*h)-(64)=0

determiningTheFunctionDomain
(h*h)-64+(5*5)=0

We add all the numbers together, and all the variables

(+h*h)-64+25=0

We add all the numbers together, and all the variables

(+h*h)-39=0

We get rid of parentheses

h*h-39=0

Wy multiply elements

h^2-39=0

a = 1; b = 0; c = -39;
Δ = b2-4ac
Δ = 02-4·1·(-39)
Δ = 156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{39}}{2*1}=\frac{0-2\sqrt{39}}{2}
=-\frac{2\sqrt{39}}{2}
=-\sqrt{39}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{39}}{2*1}=\frac{0+2\sqrt{39}}{2}
=\frac{2\sqrt{39}}{2}
=\sqrt{39}
$