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Simplifying 50x3 + -20x2 + 50x = 0 Reorder the terms: 50x + -20x2 + 50x3 = 0 Solving 50x + -20x2 + 50x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10x'. 10x(5 + -2x + 5x2) = 0 Ignore the factor 10.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 '(5 + -2x + 5x2)' equal to zero and attempt to solve: Simplifying 5 + -2x + 5x2 = 0 Solving 5 + -2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + -0.4x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.4x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -0.4x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.4x + x2 = 0 + -1 -0.4x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.4x + x2 = -1 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = -1 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = -1 + 0.04 Combine like terms: -1 + 0.04 = -0.96 0.04 + -0.4x + x2 = -0.96 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = -0.96 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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