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Simplifying x3 = 5x + -4x2 Solving x3 = 5x + -4x2 Solving for variable 'x'. Reorder the terms: -5x + 4x2 + x3 = 5x + -4x2 + -5x + 4x2 Reorder the terms: -5x + 4x2 + x3 = 5x + -5x + -4x2 + 4x2 Combine like terms: 5x + -5x = 0 -5x + 4x2 + x3 = 0 + -4x2 + 4x2 -5x + 4x2 + x3 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -5x + 4x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 4x + x2) = 0 Factor a trinomial. x((-5 + -1x)(1 + -1x)) = 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 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0, -5, 1}
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