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Simplifying 6x3 + 15x2 + 18x = 0 Reorder the terms: 18x + 15x2 + 6x3 = 0 Solving 18x + 15x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(6 + 5x + 2x2) = 0 Ignore the factor 3.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 '(6 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying 6 + 5x + 2x2 = 0 Solving 6 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + 2.5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 2.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 2.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2.5x + x2 = 0 + -3 2.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 2.5x + x2 = -3 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -3 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -3 + 1.5625 Combine like terms: -3 + 1.5625 = -1.4375 1.5625 + 2.5x + x2 = -1.4375 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = -1.4375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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