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Simplifying 3x3 + 9x2 + 42x = 0 Reorder the terms: 42x + 9x2 + 3x3 = 0 Solving 42x + 9x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(14 + 3x + x2) = 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 '(14 + 3x + x2)' equal to zero and attempt to solve: Simplifying 14 + 3x + x2 = 0 Solving 14 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 3x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 3x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 3x + x2 = 0 + -14 3x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 3x + x2 = -14 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 = -14 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -14 + 2.25 Combine like terms: -14 + 2.25 = -11.75 2.25 + 3x + x2 = -11.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -11.75 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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