$$ \color{blue}{ x_1 = 6+8i }~~ \text{and}~~ \color{blue}{ x_2 = 6-8i } $$

**Step 1:** Divide equation by a number in front of the squared term. In this case we will divide by $ 2500 $.

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

**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.

**Step 5:** Write the perfect square on the left.

**Step 6:** Take the square root of both sides.

**Step 7:** Solve for $ x $.

$ x_1,x_2 = - 6 \pm \sqrt{ -64 } $

that is,

$ x_1 = 6+8i $

$ x_2 = 6-8i $

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