12x^2=6x+11

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Solution for 12x^2=6x+11 equation:


Simplifying
12x2 = 6x + 11

Reorder the terms:
12x2 = 11 + 6x

Solving
12x2 = 11 + 6x

Solving for variable 'x'.

Reorder the terms:
-11 + -6x + 12x2 = 11 + 6x + -11 + -6x

Reorder the terms:
-11 + -6x + 12x2 = 11 + -11 + 6x + -6x

Combine like terms: 11 + -11 = 0
-11 + -6x + 12x2 = 0 + 6x + -6x
-11 + -6x + 12x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-11 + -6x + 12x2 = 0

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

Divide each side by '12'.
-0.9166666667 + -0.5x + x2 = 0

Move the constant term to the right:

Add '0.9166666667' to each side of the equation.
-0.9166666667 + -0.5x + 0.9166666667 + x2 = 0 + 0.9166666667

Reorder the terms:
-0.9166666667 + 0.9166666667 + -0.5x + x2 = 0 + 0.9166666667

Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000
0.0000000000 + -0.5x + x2 = 0 + 0.9166666667
-0.5x + x2 = 0 + 0.9166666667

Combine like terms: 0 + 0.9166666667 = 0.9166666667
-0.5x + x2 = 0.9166666667

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.9166666667 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.9166666667 + 0.0625

Combine like terms: 0.9166666667 + 0.0625 = 0.9791666667
0.0625 + -0.5x + x2 = 0.9791666667

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.9791666667

Calculate the square root of the right side: 0.989528507

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.989528507 and -0.989528507.

Subproblem 1

x + -0.25 = 0.989528507 Simplifying x + -0.25 = 0.989528507 Reorder the terms: -0.25 + x = 0.989528507 Solving -0.25 + x = 0.989528507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.989528507 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.989528507 + 0.25 x = 0.989528507 + 0.25 Combine like terms: 0.989528507 + 0.25 = 1.239528507 x = 1.239528507 Simplifying x = 1.239528507

Subproblem 2

x + -0.25 = -0.989528507 Simplifying x + -0.25 = -0.989528507 Reorder the terms: -0.25 + x = -0.989528507 Solving -0.25 + x = -0.989528507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.989528507 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.989528507 + 0.25 x = -0.989528507 + 0.25 Combine like terms: -0.989528507 + 0.25 = -0.739528507 x = -0.739528507 Simplifying x = -0.739528507

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.239528507, -0.739528507}

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