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Simplifying (6 + -24x) + -1(8x2 + 2) = 14 Remove parenthesis around (6 + -24x) 6 + -24x + -1(8x2 + 2) = 14 Reorder the terms: 6 + -24x + -1(2 + 8x2) = 14 6 + -24x + (2 * -1 + 8x2 * -1) = 14 6 + -24x + (-2 + -8x2) = 14 Reorder the terms: 6 + -2 + -24x + -8x2 = 14 Combine like terms: 6 + -2 = 4 4 + -24x + -8x2 = 14 Solving 4 + -24x + -8x2 = 14 Solving for variable 'x'. Reorder the terms: 4 + -14 + -24x + -8x2 = 14 + -14 Combine like terms: 4 + -14 = -10 -10 + -24x + -8x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -10 + -24x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + 12x + 4x2) = 0 Factor a trinomial. -2((5 + 2x)(1 + 2x)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Subproblem 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 = {-2.5, -0.5}
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