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Simplifying 20x3 + 60x2 + -216x = 0 Reorder the terms: -216x + 60x2 + 20x3 = 0 Solving -216x + 60x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-54 + 15x + 5x2) = 0 Ignore the factor 4.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 '(-54 + 15x + 5x2)' equal to zero and attempt to solve: Simplifying -54 + 15x + 5x2 = 0 Solving -54 + 15x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10.8 + 3x + x2 = 0 Move the constant term to the right: Add '10.8' to each side of the equation. -10.8 + 3x + 10.8 + x2 = 0 + 10.8 Reorder the terms: -10.8 + 10.8 + 3x + x2 = 0 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + 3x + x2 = 0 + 10.8 3x + x2 = 0 + 10.8 Combine like terms: 0 + 10.8 = 10.8 3x + x2 = 10.8 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 = 10.8 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 10.8 + 2.25 Combine like terms: 10.8 + 2.25 = 13.05 2.25 + 3x + x2 = 13.05 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 13.05 Calculate the square root of the right side: 3.612478374 Break this problem into two subproblems by setting (x + 1.5) equal to 3.612478374 and -3.612478374.Subproblem 1
x + 1.5 = 3.612478374 Simplifying x + 1.5 = 3.612478374 Reorder the terms: 1.5 + x = 3.612478374 Solving 1.5 + x = 3.612478374 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 = 3.612478374 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.612478374 + -1.5 x = 3.612478374 + -1.5 Combine like terms: 3.612478374 + -1.5 = 2.112478374 x = 2.112478374 Simplifying x = 2.112478374Subproblem 2
x + 1.5 = -3.612478374 Simplifying x + 1.5 = -3.612478374 Reorder the terms: 1.5 + x = -3.612478374 Solving 1.5 + x = -3.612478374 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 = -3.612478374 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.612478374 + -1.5 x = -3.612478374 + -1.5 Combine like terms: -3.612478374 + -1.5 = -5.112478374 x = -5.112478374 Simplifying x = -5.112478374Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.112478374, -5.112478374}Solution
x = {0, 2.112478374, -5.112478374}
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