x^2-6x=8x+80

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Solution for x^2-6x=8x+80 equation:


Simplifying
x2 + -6x = 8x + 80

Reorder the terms:
-6x + x2 = 8x + 80

Reorder the terms:
-6x + x2 = 80 + 8x

Solving
-6x + x2 = 80 + 8x

Solving for variable 'x'.

Reorder the terms:
-80 + -6x + -8x + x2 = 80 + 8x + -80 + -8x

Combine like terms: -6x + -8x = -14x
-80 + -14x + x2 = 80 + 8x + -80 + -8x

Reorder the terms:
-80 + -14x + x2 = 80 + -80 + 8x + -8x

Combine like terms: 80 + -80 = 0
-80 + -14x + x2 = 0 + 8x + -8x
-80 + -14x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-80 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -14x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + -14x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -14x + x2 = 0 + 80
-14x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
-14x + x2 = 80

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 80 + 49

Reorder the terms:
49 + -14x + x2 = 80 + 49

Combine like terms: 80 + 49 = 129
49 + -14x + x2 = 129

Factor a perfect square on the left side:
(x + -7)(x + -7) = 129

Calculate the square root of the right side: 11.357816692

Break this problem into two subproblems by setting 
(x + -7) equal to 11.357816692 and -11.357816692.

Subproblem 1

x + -7 = 11.357816692 Simplifying x + -7 = 11.357816692 Reorder the terms: -7 + x = 11.357816692 Solving -7 + x = 11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 11.357816692 + 7 Combine like terms: -7 + 7 = 0 0 + x = 11.357816692 + 7 x = 11.357816692 + 7 Combine like terms: 11.357816692 + 7 = 18.357816692 x = 18.357816692 Simplifying x = 18.357816692

Subproblem 2

x + -7 = -11.357816692 Simplifying x + -7 = -11.357816692 Reorder the terms: -7 + x = -11.357816692 Solving -7 + x = -11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -11.357816692 + 7 Combine like terms: -7 + 7 = 0 0 + x = -11.357816692 + 7 x = -11.357816692 + 7 Combine like terms: -11.357816692 + 7 = -4.357816692 x = -4.357816692 Simplifying x = -4.357816692

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.357816692, -4.357816692}

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