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Simplifying 9x3 + -105x2 + -56x = 0 Reorder the terms: -56x + -105x2 + 9x3 = 0 Solving -56x + -105x2 + 9x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-56 + -105x + 9x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-56 + -105x + 9x2)' equal to zero and attempt to solve: Simplifying -56 + -105x + 9x2 = 0 Solving -56 + -105x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -6.222222222 + -11.66666667x + x2 = 0 Move the constant term to the right: Add '6.222222222' to each side of the equation. -6.222222222 + -11.66666667x + 6.222222222 + x2 = 0 + 6.222222222 Reorder the terms: -6.222222222 + 6.222222222 + -11.66666667x + x2 = 0 + 6.222222222 Combine like terms: -6.222222222 + 6.222222222 = 0.000000000 0.000000000 + -11.66666667x + x2 = 0 + 6.222222222 -11.66666667x + x2 = 0 + 6.222222222 Combine like terms: 0 + 6.222222222 = 6.222222222 -11.66666667x + x2 = 6.222222222 The x term is -11.66666667x. Take half its coefficient (-5.833333335). Square it (34.02777780) and add it to both sides. Add '34.02777780' to each side of the equation. -11.66666667x + 34.02777780 + x2 = 6.222222222 + 34.02777780 Reorder the terms: 34.02777780 + -11.66666667x + x2 = 6.222222222 + 34.02777780 Combine like terms: 6.222222222 + 34.02777780 = 40.250000022 34.02777780 + -11.66666667x + x2 = 40.250000022 Factor a perfect square on the left side: (x + -5.833333335)(x + -5.833333335) = 40.250000022 Calculate the square root of the right side: 6.344288772 Break this problem into two subproblems by setting (x + -5.833333335) equal to 6.344288772 and -6.344288772.Subproblem 1
x + -5.833333335 = 6.344288772 Simplifying x + -5.833333335 = 6.344288772 Reorder the terms: -5.833333335 + x = 6.344288772 Solving -5.833333335 + x = 6.344288772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.833333335' to each side of the equation. -5.833333335 + 5.833333335 + x = 6.344288772 + 5.833333335 Combine like terms: -5.833333335 + 5.833333335 = 0.000000000 0.000000000 + x = 6.344288772 + 5.833333335 x = 6.344288772 + 5.833333335 Combine like terms: 6.344288772 + 5.833333335 = 12.177622107 x = 12.177622107 Simplifying x = 12.177622107Subproblem 2
x + -5.833333335 = -6.344288772 Simplifying x + -5.833333335 = -6.344288772 Reorder the terms: -5.833333335 + x = -6.344288772 Solving -5.833333335 + x = -6.344288772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.833333335' to each side of the equation. -5.833333335 + 5.833333335 + x = -6.344288772 + 5.833333335 Combine like terms: -5.833333335 + 5.833333335 = 0.000000000 0.000000000 + x = -6.344288772 + 5.833333335 x = -6.344288772 + 5.833333335 Combine like terms: -6.344288772 + 5.833333335 = -0.510955437 x = -0.510955437 Simplifying x = -0.510955437Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.177622107, -0.510955437}Solution
x = {0, 12.177622107, -0.510955437}
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