15x^2+100x-180=0

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Solution for 15x^2+100x-180=0 equation:


Simplifying
15x2 + 100x + -180 = 0

Reorder the terms:
-180 + 100x + 15x2 = 0

Solving
-180 + 100x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-36 + 20x + 3x2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-36 + 20x + 3x2)' equal to zero and attempt to solve: Simplifying -36 + 20x + 3x2 = 0 Solving -36 + 20x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -12 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 6.666666667x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 6.666666667x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 6.666666667x + x2 = 0 + 12 6.666666667x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 6.666666667x + x2 = 12 The x term is 6.666666667x. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667x + 11.11111112 + x2 = 12 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = 12 + 11.11111112 Combine like terms: 12 + 11.11111112 = 23.11111112 11.11111112 + 6.666666667x + x2 = 23.11111112 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 23.11111112 Calculate the square root of the right side: 4.807401702 Break this problem into two subproblems by setting (x + 3.333333334) equal to 4.807401702 and -4.807401702.

Subproblem 1

x + 3.333333334 = 4.807401702 Simplifying x + 3.333333334 = 4.807401702 Reorder the terms: 3.333333334 + x = 4.807401702 Solving 3.333333334 + x = 4.807401702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = 4.807401702 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 4.807401702 + -3.333333334 x = 4.807401702 + -3.333333334 Combine like terms: 4.807401702 + -3.333333334 = 1.474068368 x = 1.474068368 Simplifying x = 1.474068368

Subproblem 2

x + 3.333333334 = -4.807401702 Simplifying x + 3.333333334 = -4.807401702 Reorder the terms: 3.333333334 + x = -4.807401702 Solving 3.333333334 + x = -4.807401702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = -4.807401702 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -4.807401702 + -3.333333334 x = -4.807401702 + -3.333333334 Combine like terms: -4.807401702 + -3.333333334 = -8.140735036 x = -8.140735036 Simplifying x = -8.140735036

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.474068368, -8.140735036}

Solution

x = {1.474068368, -8.140735036}

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