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Simplifying f(0) = 10x2 + 5x + -5 Reorder the terms for easier multiplication: 0f = 10x2 + 5x + -5 Anything times zero is zero. 0f = 10x2 + 5x + -5 Reorder the terms: 0 = -5 + 5x + 10x2 Solving 0 = -5 + 5x + 10x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + -5x + -10x2 = -5 + 5x + 10x2 + 5 + -5x + -10x2 Reorder the terms: 5 + -5x + -10x2 = -5 + 5 + 5x + -5x + 10x2 + -10x2 Combine like terms: -5 + 5 = 0 5 + -5x + -10x2 = 0 + 5x + -5x + 10x2 + -10x2 5 + -5x + -10x2 = 5x + -5x + 10x2 + -10x2 Combine like terms: 5x + -5x = 0 5 + -5x + -10x2 = 0 + 10x2 + -10x2 5 + -5x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 5 + -5x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + -1x + -2x2) = 0 Factor a trinomial. 5((1 + -2x)(1 + x)) = 0 Ignore the factor 5.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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {0.5, -1}
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