(5.5)^2+x^2=(10)^2

Solution for (5.5)^2+x^2=(10)^2 equation:

(5.5)^2+x^2=(10)^2

We move all terms to the left:

(5.5)^2+x^2-((10)^2)=0

determiningTheFunctionDomain
x^2+(5.5)^2-10^2=0

We add all the numbers together, and all the variables

x^2-69.75=0

a = 1; b = 0; c = -69.75;
Δ = b2-4ac
Δ = 02-4·1·(-69.75)
Δ = 279
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:

$\sqrt{\Delta}=\sqrt{279}=\sqrt{9*31}=\sqrt{9}*\sqrt{31}=3\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{31}}{2*1}=\frac{0-3\sqrt{31}}{2}
=-\frac{3\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{31}}{2*1}=\frac{0+3\sqrt{31}}{2}
=\frac{3\sqrt{31}}{2}
$