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Simplifying 2x3 + 30x2 + -20x = 0 Reorder the terms: -20x + 30x2 + 2x3 = 0 Solving -20x + 30x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-10 + 15x + x2) = 0 Ignore the factor 2.Subproblem 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 '(-10 + 15x + x2)' equal to zero and attempt to solve: Simplifying -10 + 15x + x2 = 0 Solving -10 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 15x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 15x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 15x + x2 = 0 + 10 15x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 15x + x2 = 10 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 10 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 10 + 56.25 Combine like terms: 10 + 56.25 = 66.25 56.25 + 15x + x2 = 66.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (x + 7.5) equal to 8.139410298 and -8.139410298.Subproblem 1
x + 7.5 = 8.139410298 Simplifying x + 7.5 = 8.139410298 Reorder the terms: 7.5 + x = 8.139410298 Solving 7.5 + x = 8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 8.139410298 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 8.139410298 + -7.5 x = 8.139410298 + -7.5 Combine like terms: 8.139410298 + -7.5 = 0.639410298 x = 0.639410298 Simplifying x = 0.639410298Subproblem 2
x + 7.5 = -8.139410298 Simplifying x + 7.5 = -8.139410298 Reorder the terms: 7.5 + x = -8.139410298 Solving 7.5 + x = -8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -8.139410298 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -8.139410298 + -7.5 x = -8.139410298 + -7.5 Combine like terms: -8.139410298 + -7.5 = -15.639410298 x = -15.639410298 Simplifying x = -15.639410298Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.639410298, -15.639410298}Solution
x = {0, 0.639410298, -15.639410298}
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