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Simplifying 6x3 + x2 + 5x = 0 Reorder the terms: 5x + x2 + 6x3 = 0 Solving 5x + x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + x + 6x2) = 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 '(5 + x + 6x2)' equal to zero and attempt to solve: Simplifying 5 + x + 6x2 = 0 Solving 5 + x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 0.1666666667x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 0.1666666667x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 0.1666666667x + x2 = 0 + -0.8333333333 0.1666666667x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 0.1666666667x + x2 = -0.8333333333 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. 0.1666666667x + 0.25 + x2 = -0.8333333333 + 0.25 Reorder the terms: 0.25 + 0.1666666667x + x2 = -0.8333333333 + 0.25 Combine like terms: -0.8333333333 + 0.25 = -0.5833333333 0.25 + 0.1666666667x + x2 = -0.5833333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.5833333333 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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