12x^2-8x-122=0

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Solution for 12x^2-8x-122=0 equation:


Simplifying
12x2 + -8x + -122 = 0

Reorder the terms:
-122 + -8x + 12x2 = 0

Solving
-122 + -8x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-61 + -4x + 6x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-61 + -4x + 6x2)' equal to zero and attempt to solve: Simplifying -61 + -4x + 6x2 = 0 Solving -61 + -4x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -10.16666667 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '10.16666667' to each side of the equation. -10.16666667 + -0.6666666667x + 10.16666667 + x2 = 0 + 10.16666667 Reorder the terms: -10.16666667 + 10.16666667 + -0.6666666667x + x2 = 0 + 10.16666667 Combine like terms: -10.16666667 + 10.16666667 = 0.00000000 0.00000000 + -0.6666666667x + x2 = 0 + 10.16666667 -0.6666666667x + x2 = 0 + 10.16666667 Combine like terms: 0 + 10.16666667 = 10.16666667 -0.6666666667x + x2 = 10.16666667 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 10.16666667 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 10.16666667 + 0.1111111112 Combine like terms: 10.16666667 + 0.1111111112 = 10.2777777812 0.1111111112 + -0.6666666667x + x2 = 10.2777777812 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 10.2777777812 Calculate the square root of the right side: 3.205897344 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 3.205897344 and -3.205897344.

Subproblem 1

x + -0.3333333334 = 3.205897344 Simplifying x + -0.3333333334 = 3.205897344 Reorder the terms: -0.3333333334 + x = 3.205897344 Solving -0.3333333334 + x = 3.205897344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 3.205897344 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 3.205897344 + 0.3333333334 x = 3.205897344 + 0.3333333334 Combine like terms: 3.205897344 + 0.3333333334 = 3.5392306774 x = 3.5392306774 Simplifying x = 3.5392306774

Subproblem 2

x + -0.3333333334 = -3.205897344 Simplifying x + -0.3333333334 = -3.205897344 Reorder the terms: -0.3333333334 + x = -3.205897344 Solving -0.3333333334 + x = -3.205897344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -3.205897344 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -3.205897344 + 0.3333333334 x = -3.205897344 + 0.3333333334 Combine like terms: -3.205897344 + 0.3333333334 = -2.8725640106 x = -2.8725640106 Simplifying x = -2.8725640106

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.5392306774, -2.8725640106}

Solution

x = {3.5392306774, -2.8725640106}

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