12x^2+8x=118

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Solution for 12x^2+8x=118 equation:


Simplifying
12x2 + 8x = 118

Reorder the terms:
8x + 12x2 = 118

Solving
8x + 12x2 = 118

Solving for variable 'x'.

Reorder the terms:
-118 + 8x + 12x2 = 118 + -118

Combine like terms: 118 + -118 = 0
-118 + 8x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-59 + 4x + 6x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-59 + 4x + 6x2)' equal to zero and attempt to solve: Simplifying -59 + 4x + 6x2 = 0 Solving -59 + 4x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -9.833333333 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '9.833333333' to each side of the equation. -9.833333333 + 0.6666666667x + 9.833333333 + x2 = 0 + 9.833333333 Reorder the terms: -9.833333333 + 9.833333333 + 0.6666666667x + x2 = 0 + 9.833333333 Combine like terms: -9.833333333 + 9.833333333 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + 9.833333333 0.6666666667x + x2 = 0 + 9.833333333 Combine like terms: 0 + 9.833333333 = 9.833333333 0.6666666667x + x2 = 9.833333333 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 = 9.833333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 9.833333333 + 0.1111111112 Combine like terms: 9.833333333 + 0.1111111112 = 9.9444444442 0.1111111112 + 0.6666666667x + x2 = 9.9444444442 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 9.9444444442 Calculate the square root of the right side: 3.153481321 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 3.153481321 and -3.153481321.

Subproblem 1

x + 0.3333333334 = 3.153481321 Simplifying x + 0.3333333334 = 3.153481321 Reorder the terms: 0.3333333334 + x = 3.153481321 Solving 0.3333333334 + x = 3.153481321 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 = 3.153481321 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 3.153481321 + -0.3333333334 x = 3.153481321 + -0.3333333334 Combine like terms: 3.153481321 + -0.3333333334 = 2.8201479876 x = 2.8201479876 Simplifying x = 2.8201479876

Subproblem 2

x + 0.3333333334 = -3.153481321 Simplifying x + 0.3333333334 = -3.153481321 Reorder the terms: 0.3333333334 + x = -3.153481321 Solving 0.3333333334 + x = -3.153481321 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 = -3.153481321 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -3.153481321 + -0.3333333334 x = -3.153481321 + -0.3333333334 Combine like terms: -3.153481321 + -0.3333333334 = -3.4868146544 x = -3.4868146544 Simplifying x = -3.4868146544

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.8201479876, -3.4868146544}

Solution

x = {2.8201479876, -3.4868146544}

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