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Simplifying 0 = x3 + -2x2 + 5x Reorder the terms: 0 = 5x + -2x2 + x3 Solving 0 = 5x + -2x2 + x3 Solving for variable 'x'. Remove the zero: -5x + 2x2 + -1x3 = 5x + -2x2 + x3 + -5x + 2x2 + -1x3 Reorder the terms: -5x + 2x2 + -1x3 = 5x + -5x + -2x2 + 2x2 + x3 + -1x3 Combine like terms: 5x + -5x = 0 -5x + 2x2 + -1x3 = 0 + -2x2 + 2x2 + x3 + -1x3 -5x + 2x2 + -1x3 = -2x2 + 2x2 + x3 + -1x3 Combine like terms: -2x2 + 2x2 = 0 -5x + 2x2 + -1x3 = 0 + x3 + -1x3 -5x + 2x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -5x + 2x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 2x + -1x2) = 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 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying -5 + 2x + -1x2 = 0 Solving -5 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -2x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -2x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -2x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x + x2 = 0 + -5 -2x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -2x + x2 = -5 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 = -5 + 1 Reorder the terms: 1 + -2x + x2 = -5 + 1 Combine like terms: -5 + 1 = -4 1 + -2x + x2 = -4 Factor a perfect square on the left side: (x + -1)(x + -1) = -4 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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