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Simplifying 0 = 5x(x2 + -4x + 5) Reorder the terms: 0 = 5x(5 + -4x + x2) 0 = (5 * 5x + -4x * 5x + x2 * 5x) 0 = (25x + -20x2 + 5x3) Solving 0 = 25x + -20x2 + 5x3 Solving for variable 'x'. Remove the zero: -25x + 20x2 + -5x3 = 25x + -20x2 + 5x3 + -25x + 20x2 + -5x3 Reorder the terms: -25x + 20x2 + -5x3 = 25x + -25x + -20x2 + 20x2 + 5x3 + -5x3 Combine like terms: 25x + -25x = 0 -25x + 20x2 + -5x3 = 0 + -20x2 + 20x2 + 5x3 + -5x3 -25x + 20x2 + -5x3 = -20x2 + 20x2 + 5x3 + -5x3 Combine like terms: -20x2 + 20x2 = 0 -25x + 20x2 + -5x3 = 0 + 5x3 + -5x3 -25x + 20x2 + -5x3 = 5x3 + -5x3 Combine like terms: 5x3 + -5x3 = 0 -25x + 20x2 + -5x3 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(-5 + 4x + -1x2) = 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 '(-5 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying -5 + 4x + -1x2 = 0 Solving -5 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -4x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -4x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -4x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x + x2 = 0 + -5 -4x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -4x + x2 = -5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -5 + 4 Reorder the terms: 4 + -4x + x2 = -5 + 4 Combine like terms: -5 + 4 = -1 4 + -4x + x2 = -1 Factor a perfect square on the left side: (x + -2)(x + -2) = -1 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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