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Simplifying 2x3 + 12x2 + 32x = 0 Reorder the terms: 32x + 12x2 + 2x3 = 0 Solving 32x + 12x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(16 + 6x + x2) = 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 '(16 + 6x + x2)' equal to zero and attempt to solve: Simplifying 16 + 6x + x2 = 0 Solving 16 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 6x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 6x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 6x + x2 = 0 + -16 6x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 6x + x2 = -16 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -16 + 9 Reorder the terms: 9 + 6x + x2 = -16 + 9 Combine like terms: -16 + 9 = -7 9 + 6x + x2 = -7 Factor a perfect square on the left side: (x + 3)(x + 3) = -7 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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