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Simplifying 4x3 + 8x2 + 5x = 0 Reorder the terms: 5x + 8x2 + 4x3 = 0 Solving 5x + 8x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + 8x + 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 '(5 + 8x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + 8x + 4x2 = 0 Solving 5 + 8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 2x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 2x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 2x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 2x + x2 = 0 + -1.25 2x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 2x + x2 = -1.25 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -1.25 + 1 Reorder the terms: 1 + 2x + x2 = -1.25 + 1 Combine like terms: -1.25 + 1 = -0.25 1 + 2x + x2 = -0.25 Factor a perfect square on the left side: (x + 1)(x + 1) = -0.25 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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