4x^2-40x+25-x^2-12x+36=80

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Solution for 4x^2-40x+25-x^2-12x+36=80 equation:


Simplifying
4x2 + -40x + 25 + -1x2 + -12x + 36 = 80

Reorder the terms:
25 + 36 + -40x + -12x + 4x2 + -1x2 = 80

Combine like terms: 25 + 36 = 61
61 + -40x + -12x + 4x2 + -1x2 = 80

Combine like terms: -40x + -12x = -52x
61 + -52x + 4x2 + -1x2 = 80

Combine like terms: 4x2 + -1x2 = 3x2
61 + -52x + 3x2 = 80

Solving
61 + -52x + 3x2 = 80

Solving for variable 'x'.

Reorder the terms:
61 + -80 + -52x + 3x2 = 80 + -80

Combine like terms: 61 + -80 = -19
-19 + -52x + 3x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-19 + -52x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-6.333333333 + -17.33333333x + x2 = 0

Move the constant term to the right:

Add '6.333333333' to each side of the equation.
-6.333333333 + -17.33333333x + 6.333333333 + x2 = 0 + 6.333333333

Reorder the terms:
-6.333333333 + 6.333333333 + -17.33333333x + x2 = 0 + 6.333333333

Combine like terms: -6.333333333 + 6.333333333 = 0.000000000
0.000000000 + -17.33333333x + x2 = 0 + 6.333333333
-17.33333333x + x2 = 0 + 6.333333333

Combine like terms: 0 + 6.333333333 = 6.333333333
-17.33333333x + x2 = 6.333333333

The x term is -17.33333333x.  Take half its coefficient (-8.666666665).
Square it (75.11111108) and add it to both sides.

Add '75.11111108' to each side of the equation.
-17.33333333x + 75.11111108 + x2 = 6.333333333 + 75.11111108

Reorder the terms:
75.11111108 + -17.33333333x + x2 = 6.333333333 + 75.11111108

Combine like terms: 6.333333333 + 75.11111108 = 81.444444413
75.11111108 + -17.33333333x + x2 = 81.444444413

Factor a perfect square on the left side:
(x + -8.666666665)(x + -8.666666665) = 81.444444413

Calculate the square root of the right side: 9.024657579

Break this problem into two subproblems by setting 
(x + -8.666666665) equal to 9.024657579 and -9.024657579.

Subproblem 1

x + -8.666666665 = 9.024657579 Simplifying x + -8.666666665 = 9.024657579 Reorder the terms: -8.666666665 + x = 9.024657579 Solving -8.666666665 + x = 9.024657579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.666666665' to each side of the equation. -8.666666665 + 8.666666665 + x = 9.024657579 + 8.666666665 Combine like terms: -8.666666665 + 8.666666665 = 0.000000000 0.000000000 + x = 9.024657579 + 8.666666665 x = 9.024657579 + 8.666666665 Combine like terms: 9.024657579 + 8.666666665 = 17.691324244 x = 17.691324244 Simplifying x = 17.691324244

Subproblem 2

x + -8.666666665 = -9.024657579 Simplifying x + -8.666666665 = -9.024657579 Reorder the terms: -8.666666665 + x = -9.024657579 Solving -8.666666665 + x = -9.024657579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.666666665' to each side of the equation. -8.666666665 + 8.666666665 + x = -9.024657579 + 8.666666665 Combine like terms: -8.666666665 + 8.666666665 = 0.000000000 0.000000000 + x = -9.024657579 + 8.666666665 x = -9.024657579 + 8.666666665 Combine like terms: -9.024657579 + 8.666666665 = -0.357990914 x = -0.357990914 Simplifying x = -0.357990914

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.691324244, -0.357990914}

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