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Simplifying 5x3 + x2 + 6x = 0 Reorder the terms: 6x + x2 + 5x3 = 0 Solving 6x + x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(6 + x + 5x2) = 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 '(6 + x + 5x2)' equal to zero and attempt to solve: Simplifying 6 + x + 5x2 = 0 Solving 6 + x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + 0.2x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + 0.2x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + 0.2x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + 0.2x + x2 = 0 + -1.2 0.2x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 0.2x + x2 = -1.2 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.2x + 0.25 + x2 = -1.2 + 0.25 Reorder the terms: 0.25 + 0.2x + x2 = -1.2 + 0.25 Combine like terms: -1.2 + 0.25 = -0.95 0.25 + 0.2x + x2 = -0.95 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.95 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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