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Simplifying -4x2 + 15 = 8x2 + 24x Reorder the terms: 15 + -4x2 = 8x2 + 24x Reorder the terms: 15 + -4x2 = 24x + 8x2 Solving 15 + -4x2 = 24x + 8x2 Solving for variable 'x'. Reorder the terms: 15 + -24x + -4x2 + -8x2 = 24x + 8x2 + -24x + -8x2 Combine like terms: -4x2 + -8x2 = -12x2 15 + -24x + -12x2 = 24x + 8x2 + -24x + -8x2 Reorder the terms: 15 + -24x + -12x2 = 24x + -24x + 8x2 + -8x2 Combine like terms: 24x + -24x = 0 15 + -24x + -12x2 = 0 + 8x2 + -8x2 15 + -24x + -12x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 15 + -24x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -8x + -4x2) = 0 Factor a trinomial. 3((1 + -2x)(5 + 2x)) = 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 '(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 = -2.5Solution
x = {0.5, -2.5}
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