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Simplifying 4x3 + 15x2 + 18x = 0 Reorder the terms: 18x + 15x2 + 4x3 = 0 Solving 18x + 15x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(18 + 15x + 4x2) = 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 '(18 + 15x + 4x2)' equal to zero and attempt to solve: Simplifying 18 + 15x + 4x2 = 0 Solving 18 + 15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.5 + 3.75x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 3.75x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 3.75x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 3.75x + x2 = 0 + -4.5 3.75x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 3.75x + x2 = -4.5 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = -4.5 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = -4.5 + 3.515625 Combine like terms: -4.5 + 3.515625 = -0.984375 3.515625 + 3.75x + x2 = -0.984375 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = -0.984375 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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