x^2-100x+25^2=0

Solution for x^2-100x+25^2=0 equation:

x^2-100x+25^2=0

We add all the numbers together, and all the variables

x^2-100x+625=0

a = 1; b = -100; c = +625;
Δ = b2-4ac
Δ = -1002-4·1·625
Δ = 7500
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:

$\sqrt{\Delta}=\sqrt{7500}=\sqrt{2500*3}=\sqrt{2500}*\sqrt{3}=50\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-50\sqrt{3}}{2*1}=\frac{100-50\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+50\sqrt{3}}{2*1}=\frac{100+50\sqrt{3}}{2}
$