6x^2-12+8x=5

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Solution for 6x^2-12+8x=5 equation:


Simplifying
6x2 + -12 + 8x = 5

Reorder the terms:
-12 + 8x + 6x2 = 5

Solving
-12 + 8x + 6x2 = 5

Solving for variable 'x'.

Reorder the terms:
-12 + -5 + 8x + 6x2 = 5 + -5

Combine like terms: -12 + -5 = -17
-17 + 8x + 6x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-17 + 8x + 6x2 = 0

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

Divide each side by '6'.
-2.833333333 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + 1.333333333x + 2.833333333 + x2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + 1.333333333x + x2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + 1.333333333x + x2 = 0 + 2.833333333
1.333333333x + x2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
1.333333333x + x2 = 2.833333333

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 = 2.833333333 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 2.833333333 + 0.4444444442

Combine like terms: 2.833333333 + 0.4444444442 = 3.2777777772
0.4444444442 + 1.333333333x + x2 = 3.2777777772

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 3.2777777772

Calculate the square root of the right side: 1.810463415

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 1.810463415 and -1.810463415.

Subproblem 1

x + 0.6666666665 = 1.810463415 Simplifying x + 0.6666666665 = 1.810463415 Reorder the terms: 0.6666666665 + x = 1.810463415 Solving 0.6666666665 + x = 1.810463415 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 = 1.810463415 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.810463415 + -0.6666666665 x = 1.810463415 + -0.6666666665 Combine like terms: 1.810463415 + -0.6666666665 = 1.1437967485 x = 1.1437967485 Simplifying x = 1.1437967485

Subproblem 2

x + 0.6666666665 = -1.810463415 Simplifying x + 0.6666666665 = -1.810463415 Reorder the terms: 0.6666666665 + x = -1.810463415 Solving 0.6666666665 + x = -1.810463415 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 = -1.810463415 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.810463415 + -0.6666666665 x = -1.810463415 + -0.6666666665 Combine like terms: -1.810463415 + -0.6666666665 = -2.4771300815 x = -2.4771300815 Simplifying x = -2.4771300815

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.1437967485, -2.4771300815}

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