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Simplifying x3 + -24x2 + -95x = 0 Reorder the terms: -95x + -24x2 + x3 = 0 Solving -95x + -24x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-95 + -24x + x2) = 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 '(-95 + -24x + x2)' equal to zero and attempt to solve: Simplifying -95 + -24x + x2 = 0 Solving -95 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + -24x + 95 + x2 = 0 + 95 Reorder the terms: -95 + 95 + -24x + x2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + -24x + x2 = 0 + 95 -24x + x2 = 0 + 95 Combine like terms: 0 + 95 = 95 -24x + x2 = 95 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 95 + 144 Reorder the terms: 144 + -24x + x2 = 95 + 144 Combine like terms: 95 + 144 = 239 144 + -24x + x2 = 239 Factor a perfect square on the left side: (x + -12)(x + -12) = 239 Calculate the square root of the right side: 15.459624834 Break this problem into two subproblems by setting (x + -12) equal to 15.459624834 and -15.459624834.Subproblem 1
x + -12 = 15.459624834 Simplifying x + -12 = 15.459624834 Reorder the terms: -12 + x = 15.459624834 Solving -12 + x = 15.459624834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 15.459624834 + 12 Combine like terms: -12 + 12 = 0 0 + x = 15.459624834 + 12 x = 15.459624834 + 12 Combine like terms: 15.459624834 + 12 = 27.459624834 x = 27.459624834 Simplifying x = 27.459624834Subproblem 2
x + -12 = -15.459624834 Simplifying x + -12 = -15.459624834 Reorder the terms: -12 + x = -15.459624834 Solving -12 + x = -15.459624834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -15.459624834 + 12 Combine like terms: -12 + 12 = 0 0 + x = -15.459624834 + 12 x = -15.459624834 + 12 Combine like terms: -15.459624834 + 12 = -3.459624834 x = -3.459624834 Simplifying x = -3.459624834Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.459624834, -3.459624834}Solution
x = {0, 27.459624834, -3.459624834}
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