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Simplifying 8(2x2 + 3x + -2) = 0 Reorder the terms: 8(-2 + 3x + 2x2) = 0 (-2 * 8 + 3x * 8 + 2x2 * 8) = 0 (-16 + 24x + 16x2) = 0 Solving -16 + 24x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-2 + 3x + 2x2) = 0 Factor a trinomial. 8((-2 + -1x)(1 + -2x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
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 = 0.5Solution
x = {-2, 0.5}
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