x^2-12x=20

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Solution for x^2-12x=20 equation:


Simplifying
x2 + -12x = 20

Reorder the terms:
-12x + x2 = 20

Solving
-12x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + -12x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -12x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -12x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -12x + x2 = 0 + 20
-12x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-12x + x2 = 20

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = 20 + 36

Reorder the terms:
36 + -12x + x2 = 20 + 36

Combine like terms: 20 + 36 = 56
36 + -12x + x2 = 56

Factor a perfect square on the left side:
(x + -6)(x + -6) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(x + -6) equal to 7.483314774 and -7.483314774.

Subproblem 1

x + -6 = 7.483314774 Simplifying x + -6 = 7.483314774 Reorder the terms: -6 + x = 7.483314774 Solving -6 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.483314774 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.483314774 + 6 x = 7.483314774 + 6 Combine like terms: 7.483314774 + 6 = 13.483314774 x = 13.483314774 Simplifying x = 13.483314774

Subproblem 2

x + -6 = -7.483314774 Simplifying x + -6 = -7.483314774 Reorder the terms: -6 + x = -7.483314774 Solving -6 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.483314774 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.483314774 + 6 x = -7.483314774 + 6 Combine like terms: -7.483314774 + 6 = -1.483314774 x = -1.483314774 Simplifying x = -1.483314774

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.483314774, -1.483314774}

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