Step 1: We can simplify equation by multiplying both sides by -1. After multiplying we have the following equation:

$$ \begin{aligned} -x^2-10x+100 &= 0 \,\,\, / \color{orangered}{\cdot \, -1 } \\[0.9 em ] x^2+10x-100 &=0 \end{aligned} $$

Step 2: Keep all terms containing $ x $ on one side. Move $ -100 $ to the right.

$$ x^2+10x = 100 $$

Step 3: Take half of the x -term coefficient and square it. Add this value to both sides.

The x-term coefficient = $ 10 $

The half of the x-term coefficient = $ 5 $

After squaring we have $ 5^2 = 25 $

When we add $ 25 $ to both sides we have:

$$ x^2+10x+25 = 100 + 25 $$

Step 4: Simplify right side.

$$ x^2+10x+25 = 125 $$

Step 5: Write the perfect square on the left.

$$ \left(x + 5 \right)^2 = 125 $$

Step 6: Take the square root of both sides.

$$ x + 5 = \pm \sqrt { 125 } $$

Step 7: Solve for $ x $.

$ x_1,x_2 = - 5 \pm \sqrt{ 125 } $

that is,

$ x_1 = -5-5 \sqrt{ 5 } $

$ x_2 = -5+5 \sqrt{ 5 } $

Quadratic Equation Solver