x^2=1048

Solution for x^2=1048 equation:

x^2=1048

We move all terms to the left:

x^2-(1048)=0

a = 1; b = 0; c = -1048;
Δ = b2-4ac
Δ = 02-4·1·(-1048)
Δ = 4192
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:

$\sqrt{\Delta}=\sqrt{4192}=\sqrt{16*262}=\sqrt{16}*\sqrt{262}=4\sqrt{262}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{262}}{2*1}=\frac{0-4\sqrt{262}}{2}
=-\frac{4\sqrt{262}}{2}
=-2\sqrt{262}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{262}}{2*1}=\frac{0+4\sqrt{262}}{2}
=\frac{4\sqrt{262}}{2}
=2\sqrt{262}
$