0=12x^2+16x-5

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Solution for 0=12x^2+16x-5 equation:


Simplifying
0 = 12x2 + 16x + -5

Reorder the terms:
0 = -5 + 16x + 12x2

Solving
0 = -5 + 16x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + 5 = 5
5 + -16x + -12x2 = -5 + 16x + 12x2 + 5 + -16x + -12x2

Reorder the terms:
5 + -16x + -12x2 = -5 + 5 + 16x + -16x + 12x2 + -12x2

Combine like terms: -5 + 5 = 0
5 + -16x + -12x2 = 0 + 16x + -16x + 12x2 + -12x2
5 + -16x + -12x2 = 16x + -16x + 12x2 + -12x2

Combine like terms: 16x + -16x = 0
5 + -16x + -12x2 = 0 + 12x2 + -12x2
5 + -16x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
5 + -16x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-0.4166666667 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 1.333333333x + 0.4166666667 + x2 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + 1.333333333x + x2 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + 1.333333333x + x2 = 0 + 0.4166666667
1.333333333x + x2 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
1.333333333x + x2 = 0.4166666667

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 = 0.4166666667 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 0.4166666667 + 0.4444444442

Combine like terms: 0.4166666667 + 0.4444444442 = 0.8611111109
0.4444444442 + 1.333333333x + x2 = 0.8611111109

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 0.8611111109

Calculate the square root of the right side: 0.927960727

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 0.927960727 and -0.927960727.

Subproblem 1

x + 0.6666666665 = 0.927960727 Simplifying x + 0.6666666665 = 0.927960727 Reorder the terms: 0.6666666665 + x = 0.927960727 Solving 0.6666666665 + x = 0.927960727 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 = 0.927960727 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.927960727 + -0.6666666665 x = 0.927960727 + -0.6666666665 Combine like terms: 0.927960727 + -0.6666666665 = 0.2612940605 x = 0.2612940605 Simplifying x = 0.2612940605

Subproblem 2

x + 0.6666666665 = -0.927960727 Simplifying x + 0.6666666665 = -0.927960727 Reorder the terms: 0.6666666665 + x = -0.927960727 Solving 0.6666666665 + x = -0.927960727 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 = -0.927960727 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.927960727 + -0.6666666665 x = -0.927960727 + -0.6666666665 Combine like terms: -0.927960727 + -0.6666666665 = -1.5946273935 x = -1.5946273935 Simplifying x = -1.5946273935

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2612940605, -1.5946273935}

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