3x^2=26x+12

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Solution for 3x^2=26x+12 equation:


Simplifying
3x2 = 26x + 12

Reorder the terms:
3x2 = 12 + 26x

Solving
3x2 = 12 + 26x

Solving for variable 'x'.

Reorder the terms:
-12 + -26x + 3x2 = 12 + 26x + -12 + -26x

Reorder the terms:
-12 + -26x + 3x2 = 12 + -12 + 26x + -26x

Combine like terms: 12 + -12 = 0
-12 + -26x + 3x2 = 0 + 26x + -26x
-12 + -26x + 3x2 = 26x + -26x

Combine like terms: 26x + -26x = 0
-12 + -26x + 3x2 = 0

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

Divide each side by '3'.
-4 + -8.666666667x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -8.666666667x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -8.666666667x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -8.666666667x + x2 = 0 + 4
-8.666666667x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-8.666666667x + x2 = 4

The x term is -8.666666667x.  Take half its coefficient (-4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
-8.666666667x + 18.77777778 + x2 = 4 + 18.77777778

Reorder the terms:
18.77777778 + -8.666666667x + x2 = 4 + 18.77777778

Combine like terms: 4 + 18.77777778 = 22.77777778
18.77777778 + -8.666666667x + x2 = 22.77777778

Factor a perfect square on the left side:
(x + -4.333333334)(x + -4.333333334) = 22.77777778

Calculate the square root of the right side: 4.772607021

Break this problem into two subproblems by setting 
(x + -4.333333334) equal to 4.772607021 and -4.772607021.

Subproblem 1

x + -4.333333334 = 4.772607021 Simplifying x + -4.333333334 = 4.772607021 Reorder the terms: -4.333333334 + x = 4.772607021 Solving -4.333333334 + x = 4.772607021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.333333334' to each side of the equation. -4.333333334 + 4.333333334 + x = 4.772607021 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = 4.772607021 + 4.333333334 x = 4.772607021 + 4.333333334 Combine like terms: 4.772607021 + 4.333333334 = 9.105940355 x = 9.105940355 Simplifying x = 9.105940355

Subproblem 2

x + -4.333333334 = -4.772607021 Simplifying x + -4.333333334 = -4.772607021 Reorder the terms: -4.333333334 + x = -4.772607021 Solving -4.333333334 + x = -4.772607021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.333333334' to each side of the equation. -4.333333334 + 4.333333334 + x = -4.772607021 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = -4.772607021 + 4.333333334 x = -4.772607021 + 4.333333334 Combine like terms: -4.772607021 + 4.333333334 = -0.439273687 x = -0.439273687 Simplifying x = -0.439273687

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.105940355, -0.439273687}

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