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Simplifying P(0) = -2x2 + 24x + -54 Reorder the terms for easier multiplication: 0P = -2x2 + 24x + -54 Anything times zero is zero. 0P = -2x2 + 24x + -54 Reorder the terms: 0 = -54 + 24x + -2x2 Solving 0 = -54 + 24x + -2x2 Solving for variable 'x'. Combine like terms: 0 + 54 = 54 54 + -24x + 2x2 = -54 + 24x + -2x2 + 54 + -24x + 2x2 Reorder the terms: 54 + -24x + 2x2 = -54 + 54 + 24x + -24x + -2x2 + 2x2 Combine like terms: -54 + 54 = 0 54 + -24x + 2x2 = 0 + 24x + -24x + -2x2 + 2x2 54 + -24x + 2x2 = 24x + -24x + -2x2 + 2x2 Combine like terms: 24x + -24x = 0 54 + -24x + 2x2 = 0 + -2x2 + 2x2 54 + -24x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 54 + -24x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -12x + x2) = 0 Factor a trinomial. 2((3 + -1x)(9 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {3, 9}
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