36x^2+96x-24=0

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Solution for 36x^2+96x-24=0 equation:


Simplifying
36x2 + 96x + -24 = 0

Reorder the terms:
-24 + 96x + 36x2 = 0

Solving
-24 + 96x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-2 + 8x + 3x2) = 0

Ignore the factor 12.

Subproblem 1

Set the factor '(-2 + 8x + 3x2)' equal to zero and attempt to solve: Simplifying -2 + 8x + 3x2 = 0 Solving -2 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 2.666666667x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 2.666666667x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 2.666666667x + x2 = 0 + 0.6666666667 2.666666667x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 2.666666667x + x2 = 0.6666666667 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 0.6666666667 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 0.6666666667 + 1.777777780 Combine like terms: 0.6666666667 + 1.777777780 = 2.4444444467 1.777777780 + 2.666666667x + x2 = 2.4444444467 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 2.4444444467 Calculate the square root of the right side: 1.563471921 Break this problem into two subproblems by setting (x + 1.333333334) equal to 1.563471921 and -1.563471921.

Subproblem 1

x + 1.333333334 = 1.563471921 Simplifying x + 1.333333334 = 1.563471921 Reorder the terms: 1.333333334 + x = 1.563471921 Solving 1.333333334 + x = 1.563471921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 1.563471921 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.563471921 + -1.333333334 x = 1.563471921 + -1.333333334 Combine like terms: 1.563471921 + -1.333333334 = 0.230138587 x = 0.230138587 Simplifying x = 0.230138587

Subproblem 2

x + 1.333333334 = -1.563471921 Simplifying x + 1.333333334 = -1.563471921 Reorder the terms: 1.333333334 + x = -1.563471921 Solving 1.333333334 + x = -1.563471921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -1.563471921 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.563471921 + -1.333333334 x = -1.563471921 + -1.333333334 Combine like terms: -1.563471921 + -1.333333334 = -2.896805255 x = -2.896805255 Simplifying x = -2.896805255

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.230138587, -2.896805255}

Solution

x = {0.230138587, -2.896805255}

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