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Simplifying x3 + -13x2 + -40x = 0 Reorder the terms: -40x + -13x2 + x3 = 0 Solving -40x + -13x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-40 + -13x + 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 '(-40 + -13x + x2)' equal to zero and attempt to solve: Simplifying -40 + -13x + x2 = 0 Solving -40 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -13x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -13x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -13x + x2 = 0 + 40 -13x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -13x + x2 = 40 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 40 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 40 + 42.25 Combine like terms: 40 + 42.25 = 82.25 42.25 + -13x + x2 = 82.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x + -6.5) equal to 9.069178574 and -9.069178574.Subproblem 1
x + -6.5 = 9.069178574 Simplifying x + -6.5 = 9.069178574 Reorder the terms: -6.5 + x = 9.069178574 Solving -6.5 + x = 9.069178574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 9.069178574 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 9.069178574 + 6.5 x = 9.069178574 + 6.5 Combine like terms: 9.069178574 + 6.5 = 15.569178574 x = 15.569178574 Simplifying x = 15.569178574Subproblem 2
x + -6.5 = -9.069178574 Simplifying x + -6.5 = -9.069178574 Reorder the terms: -6.5 + x = -9.069178574 Solving -6.5 + x = -9.069178574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -9.069178574 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -9.069178574 + 6.5 x = -9.069178574 + 6.5 Combine like terms: -9.069178574 + 6.5 = -2.569178574 x = -2.569178574 Simplifying x = -2.569178574Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.569178574, -2.569178574}Solution
x = {0, 15.569178574, -2.569178574}
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