x*x=547

Solution for x*x=547 equation:

x*x=547

We move all terms to the left:

x*x-(547)=0

Wy multiply elements

x^2-547=0

a = 1; b = 0; c = -547;
Δ = b2-4ac
Δ = 02-4·1·(-547)
Δ = 2188
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:

$\sqrt{\Delta}=\sqrt{2188}=\sqrt{4*547}=\sqrt{4}*\sqrt{547}=2\sqrt{547}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{547}}{2*1}=\frac{0-2\sqrt{547}}{2}
=-\frac{2\sqrt{547}}{2}
=-\sqrt{547}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{547}}{2*1}=\frac{0+2\sqrt{547}}{2}
=\frac{2\sqrt{547}}{2}
=\sqrt{547}
$