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Simplifying 0 = 12x2 + -80x + -96 Reorder the terms: 0 = -96 + -80x + 12x2 Solving 0 = -96 + -80x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 96 = 96 96 + 80x + -12x2 = -96 + -80x + 12x2 + 96 + 80x + -12x2 Reorder the terms: 96 + 80x + -12x2 = -96 + 96 + -80x + 80x + 12x2 + -12x2 Combine like terms: -96 + 96 = 0 96 + 80x + -12x2 = 0 + -80x + 80x + 12x2 + -12x2 96 + 80x + -12x2 = -80x + 80x + 12x2 + -12x2 Combine like terms: -80x + 80x = 0 96 + 80x + -12x2 = 0 + 12x2 + -12x2 96 + 80x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 96 + 80x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(24 + 20x + -3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(24 + 20x + -3x2)' equal to zero and attempt to solve: Simplifying 24 + 20x + -3x2 = 0 Solving 24 + 20x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -8 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -6.666666667x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -6.666666667x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -6.666666667x + x2 = 0 + 8 -6.666666667x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -6.666666667x + x2 = 8 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 = 8 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = 8 + 11.11111112 Combine like terms: 8 + 11.11111112 = 19.11111112 11.11111112 + -6.666666667x + x2 = 19.11111112 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = 19.11111112 Calculate the square root of the right side: 4.371625684 Break this problem into two subproblems by setting (x + -3.333333334) equal to 4.371625684 and -4.371625684.Subproblem 1
x + -3.333333334 = 4.371625684 Simplifying x + -3.333333334 = 4.371625684 Reorder the terms: -3.333333334 + x = 4.371625684 Solving -3.333333334 + x = 4.371625684 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 = 4.371625684 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 4.371625684 + 3.333333334 x = 4.371625684 + 3.333333334 Combine like terms: 4.371625684 + 3.333333334 = 7.704959018 x = 7.704959018 Simplifying x = 7.704959018Subproblem 2
x + -3.333333334 = -4.371625684 Simplifying x + -3.333333334 = -4.371625684 Reorder the terms: -3.333333334 + x = -4.371625684 Solving -3.333333334 + x = -4.371625684 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 = -4.371625684 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -4.371625684 + 3.333333334 x = -4.371625684 + 3.333333334 Combine like terms: -4.371625684 + 3.333333334 = -1.03829235 x = -1.03829235 Simplifying x = -1.03829235Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.704959018, -1.03829235}Solution
x = {7.704959018, -1.03829235}
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