Step 1: Divide equation by a number in front of the squared term. In this case we will divide by $ 2500 $.
$$ \begin{aligned} 2500x^2-30000x+250000 &= 0 \,\,\, ( \color{orangered}{ : 2500 } ) \\[0.9 em ] x^2-12x+100 &=0 \end{aligned} $$Step 2: Keep all terms containing $ x $ on one side. Move $ 100 $ to the right.
$$ x^2-12x = -100 $$Step 3: Take half of the x -term coefficient and square it. Add this value to both sides.
The x-term coefficient = $ -12 $
The half of the x-term coefficient = $ -6 $
After squaring we have $ (-6)^2 = 36 $
When we add $ 36 $ to both sides we have:
$$ x^2-12x+36 = -100 + 36 $$Step 4: Simplify right side.
$$ x^2-12x+36 = -64 $$Step 5: Write the perfect square on the left.
$$ \left(x + 6 \right)^2 = -64 $$Step 6: Take the square root of both sides.
$$ x + 6 = \pm \sqrt { -64 } $$Step 7: Solve for $ x $.
$ x_1,x_2 = - 6 \pm \sqrt{ -64 } $
that is,
$ x_1 = 6+8i $
$ x_2 = 6-8i $