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Simplifying f(0) = 6x2 + 45x + -24 Reorder the terms for easier multiplication: 0f = 6x2 + 45x + -24 Anything times zero is zero. 0f = 6x2 + 45x + -24 Reorder the terms: 0 = -24 + 45x + 6x2 Solving 0 = -24 + 45x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 24 = 24 24 + -45x + -6x2 = -24 + 45x + 6x2 + 24 + -45x + -6x2 Reorder the terms: 24 + -45x + -6x2 = -24 + 24 + 45x + -45x + 6x2 + -6x2 Combine like terms: -24 + 24 = 0 24 + -45x + -6x2 = 0 + 45x + -45x + 6x2 + -6x2 24 + -45x + -6x2 = 45x + -45x + 6x2 + -6x2 Combine like terms: 45x + -45x = 0 24 + -45x + -6x2 = 0 + 6x2 + -6x2 24 + -45x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 24 + -45x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(8 + -15x + -2x2) = 0 Factor a trinomial. 3((1 + -2x)(8 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Solution
x = {0.5, -8}
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