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Simplifying 5x(4x2 + -3x + 1) = 0 Reorder the terms: 5x(1 + -3x + 4x2) = 0 (1 * 5x + -3x * 5x + 4x2 * 5x) = 0 (5x + -15x2 + 20x3) = 0 Solving 5x + -15x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(1 + -3x + 4x2) = 0 Ignore the factor 5.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 '(1 + -3x + 4x2)' equal to zero and attempt to solve: Simplifying 1 + -3x + 4x2 = 0 Solving 1 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -0.75x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -0.75x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -0.75x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -0.75x + x2 = 0 + -0.25 -0.75x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -0.75x + x2 = -0.25 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -0.25 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -0.25 + 0.140625 Combine like terms: -0.25 + 0.140625 = -0.109375 0.140625 + -0.75x + x2 = -0.109375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -0.109375 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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