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Simplifying x3 + 3x2 + -216x = 0 Reorder the terms: -216x + 3x2 + x3 = 0 Solving -216x + 3x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-216 + 3x + 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 '(-216 + 3x + x2)' equal to zero and attempt to solve: Simplifying -216 + 3x + x2 = 0 Solving -216 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '216' to each side of the equation. -216 + 3x + 216 + x2 = 0 + 216 Reorder the terms: -216 + 216 + 3x + x2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + 3x + x2 = 0 + 216 3x + x2 = 0 + 216 Combine like terms: 0 + 216 = 216 3x + x2 = 216 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 216 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 216 + 2.25 Combine like terms: 216 + 2.25 = 218.25 2.25 + 3x + x2 = 218.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 218.25 Calculate the square root of the right side: 14.773286703 Break this problem into two subproblems by setting (x + 1.5) equal to 14.773286703 and -14.773286703.Subproblem 1
x + 1.5 = 14.773286703 Simplifying x + 1.5 = 14.773286703 Reorder the terms: 1.5 + x = 14.773286703 Solving 1.5 + x = 14.773286703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 14.773286703 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 14.773286703 + -1.5 x = 14.773286703 + -1.5 Combine like terms: 14.773286703 + -1.5 = 13.273286703 x = 13.273286703 Simplifying x = 13.273286703Subproblem 2
x + 1.5 = -14.773286703 Simplifying x + 1.5 = -14.773286703 Reorder the terms: 1.5 + x = -14.773286703 Solving 1.5 + x = -14.773286703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -14.773286703 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -14.773286703 + -1.5 x = -14.773286703 + -1.5 Combine like terms: -14.773286703 + -1.5 = -16.273286703 x = -16.273286703 Simplifying x = -16.273286703Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.273286703, -16.273286703}Solution
x = {0, 13.273286703, -16.273286703}
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