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Simplifying x3 + 9x + -27 = (x2 + -1x + 9)(x + -3) Reorder the terms: -27 + 9x + x3 = (x2 + -1x + 9)(x + -3) Reorder the terms: -27 + 9x + x3 = (9 + -1x + x2)(x + -3) Reorder the terms: -27 + 9x + x3 = (9 + -1x + x2)(-3 + x) Multiply (9 + -1x + x2) * (-3 + x) -27 + 9x + x3 = (9(-3 + x) + -1x * (-3 + x) + x2(-3 + x)) -27 + 9x + x3 = ((-3 * 9 + x * 9) + -1x * (-3 + x) + x2(-3 + x)) -27 + 9x + x3 = ((-27 + 9x) + -1x * (-3 + x) + x2(-3 + x)) -27 + 9x + x3 = (-27 + 9x + (-3 * -1x + x * -1x) + x2(-3 + x)) -27 + 9x + x3 = (-27 + 9x + (3x + -1x2) + x2(-3 + x)) -27 + 9x + x3 = (-27 + 9x + 3x + -1x2 + (-3 * x2 + x * x2)) -27 + 9x + x3 = (-27 + 9x + 3x + -1x2 + (-3x2 + x3)) Combine like terms: 9x + 3x = 12x -27 + 9x + x3 = (-27 + 12x + -1x2 + -3x2 + x3) Combine like terms: -1x2 + -3x2 = -4x2 -27 + 9x + x3 = (-27 + 12x + -4x2 + x3) Add '27' to each side of the equation. -27 + 9x + 27 + x3 = -27 + 12x + -4x2 + 27 + x3 Reorder the terms: -27 + 27 + 9x + x3 = -27 + 12x + -4x2 + 27 + x3 Combine like terms: -27 + 27 = 0 0 + 9x + x3 = -27 + 12x + -4x2 + 27 + x3 9x + x3 = -27 + 12x + -4x2 + 27 + x3 Reorder the terms: 9x + x3 = -27 + 27 + 12x + -4x2 + x3 Combine like terms: -27 + 27 = 0 9x + x3 = 0 + 12x + -4x2 + x3 9x + x3 = 12x + -4x2 + x3 Add '-1x3' to each side of the equation. 9x + x3 + -1x3 = 12x + -4x2 + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 9x + 0 = 12x + -4x2 + x3 + -1x3 9x = 12x + -4x2 + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 9x = 12x + -4x2 + 0 9x = 12x + -4x2 Solving 9x = 12x + -4x2 Solving for variable 'x'. Combine like terms: 9x + -12x = -3x -3x + 4x2 = 12x + -4x2 + -12x + 4x2 Reorder the terms: -3x + 4x2 = 12x + -12x + -4x2 + 4x2 Combine like terms: 12x + -12x = 0 -3x + 4x2 = 0 + -4x2 + 4x2 -3x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -3x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + 4x) = 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 '(-3 + 4x)' equal to zero and attempt to solve: Simplifying -3 + 4x = 0 Solving -3 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4x = 0 + 3 4x = 0 + 3 Combine like terms: 0 + 3 = 3 4x = 3 Divide each side by '4'. x = 0.75 Simplifying x = 0.75Solution
x = {0, 0.75}
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