x2+(.05x)2=361

Solution for x2+(.05x)2=361 equation:

x2+(.05x)2=361

We move all terms to the left:

x2+(.05x)2-(361)=0

We add all the numbers together, and all the variables

x2+(+.05x)2-361=0

We add all the numbers together, and all the variables

x^2+(+.05x)2-361=0

We multiply parentheses

x^2+2x-361=0

a = 1; b = 2; c = -361;
Δ = b2-4ac
Δ = 22-4·1·(-361)
Δ = 1448
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:

$\sqrt{\Delta}=\sqrt{1448}=\sqrt{4*362}=\sqrt{4}*\sqrt{362}=2\sqrt{362}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{362}}{2*1}=\frac{-2-2\sqrt{362}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{362}}{2*1}=\frac{-2+2\sqrt{362}}{2}
$