x^2-20x=20x+100

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Solution for x^2-20x=20x+100 equation:


Simplifying
x2 + -20x = 20x + 100

Reorder the terms:
-20x + x2 = 20x + 100

Reorder the terms:
-20x + x2 = 100 + 20x

Solving
-20x + x2 = 100 + 20x

Solving for variable 'x'.

Reorder the terms:
-100 + -20x + -20x + x2 = 100 + 20x + -100 + -20x

Combine like terms: -20x + -20x = -40x
-100 + -40x + x2 = 100 + 20x + -100 + -20x

Reorder the terms:
-100 + -40x + x2 = 100 + -100 + 20x + -20x

Combine like terms: 100 + -100 = 0
-100 + -40x + x2 = 0 + 20x + -20x
-100 + -40x + x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
-100 + -40x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -40x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + -40x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -40x + x2 = 0 + 100
-40x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
-40x + x2 = 100

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = 100 + 400

Reorder the terms:
400 + -40x + x2 = 100 + 400

Combine like terms: 100 + 400 = 500
400 + -40x + x2 = 500

Factor a perfect square on the left side:
(x + -20)(x + -20) = 500

Calculate the square root of the right side: 22.360679775

Break this problem into two subproblems by setting 
(x + -20) equal to 22.360679775 and -22.360679775.

Subproblem 1

x + -20 = 22.360679775 Simplifying x + -20 = 22.360679775 Reorder the terms: -20 + x = 22.360679775 Solving -20 + x = 22.360679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 22.360679775 + 20 Combine like terms: -20 + 20 = 0 0 + x = 22.360679775 + 20 x = 22.360679775 + 20 Combine like terms: 22.360679775 + 20 = 42.360679775 x = 42.360679775 Simplifying x = 42.360679775

Subproblem 2

x + -20 = -22.360679775 Simplifying x + -20 = -22.360679775 Reorder the terms: -20 + x = -22.360679775 Solving -20 + x = -22.360679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -22.360679775 + 20 Combine like terms: -20 + 20 = 0 0 + x = -22.360679775 + 20 x = -22.360679775 + 20 Combine like terms: -22.360679775 + 20 = -2.360679775 x = -2.360679775 Simplifying x = -2.360679775

Solution

The solution to the problem is based on the solutions from the subproblems. x = {42.360679775, -2.360679775}

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