-8x+10-3x^2=-12x

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Solution for -8x+10-3x^2=-12x equation:


Simplifying
-8x + 10 + -3x2 = -12x

Reorder the terms:
10 + -8x + -3x2 = -12x

Solving
10 + -8x + -3x2 = -12x

Solving for variable 'x'.

Reorder the terms:
10 + -8x + 12x + -3x2 = -12x + 12x

Combine like terms: -8x + 12x = 4x
10 + 4x + -3x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
10 + 4x + -3x2 = 0

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

Divide each side by '-3'.
-3.333333333 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -1.333333333x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -1.333333333x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + 3.333333333
-1.333333333x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-1.333333333x + x2 = 3.333333333

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 3.333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 3.333333333 + 0.4444444442

Combine like terms: 3.333333333 + 0.4444444442 = 3.7777777772
0.4444444442 + -1.333333333x + x2 = 3.7777777772

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 3.7777777772

Calculate the square root of the right side: 1.943650631

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 1.943650631 and -1.943650631.

Subproblem 1

x + -0.6666666665 = 1.943650631 Simplifying x + -0.6666666665 = 1.943650631 Reorder the terms: -0.6666666665 + x = 1.943650631 Solving -0.6666666665 + x = 1.943650631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 1.943650631 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.943650631 + 0.6666666665 x = 1.943650631 + 0.6666666665 Combine like terms: 1.943650631 + 0.6666666665 = 2.6103172975 x = 2.6103172975 Simplifying x = 2.6103172975

Subproblem 2

x + -0.6666666665 = -1.943650631 Simplifying x + -0.6666666665 = -1.943650631 Reorder the terms: -0.6666666665 + x = -1.943650631 Solving -0.6666666665 + x = -1.943650631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -1.943650631 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.943650631 + 0.6666666665 x = -1.943650631 + 0.6666666665 Combine like terms: -1.943650631 + 0.6666666665 = -1.2769839645 x = -1.2769839645 Simplifying x = -1.2769839645

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.6103172975, -1.2769839645}

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