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Simplifying 4x3 + 18x2 + -24x = 0 Reorder the terms: -24x + 18x2 + 4x3 = 0 Solving -24x + 18x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-12 + 9x + 2x2) = 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 '(-12 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying -12 + 9x + 2x2 = 0 Solving -12 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + 4.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 4.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 4.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4.5x + x2 = 0 + 6 4.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 4.5x + x2 = 6 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 6 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 6 + 5.0625 Combine like terms: 6 + 5.0625 = 11.0625 5.0625 + 4.5x + x2 = 11.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (x + 2.25) equal to 3.326033674 and -3.326033674.Subproblem 1
x + 2.25 = 3.326033674 Simplifying x + 2.25 = 3.326033674 Reorder the terms: 2.25 + x = 3.326033674 Solving 2.25 + x = 3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.326033674 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.326033674 + -2.25 x = 3.326033674 + -2.25 Combine like terms: 3.326033674 + -2.25 = 1.076033674 x = 1.076033674 Simplifying x = 1.076033674Subproblem 2
x + 2.25 = -3.326033674 Simplifying x + 2.25 = -3.326033674 Reorder the terms: 2.25 + x = -3.326033674 Solving 2.25 + x = -3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.326033674 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.326033674 + -2.25 x = -3.326033674 + -2.25 Combine like terms: -3.326033674 + -2.25 = -5.576033674 x = -5.576033674 Simplifying x = -5.576033674Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.076033674, -5.576033674}Solution
x = {0, 1.076033674, -5.576033674}
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