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Simplifying 24x2 + 6x = 9 Reorder the terms: 6x + 24x2 = 9 Solving 6x + 24x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 6x + 24x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 6x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 2x + 8x2) = 0 Factor a trinomial. 3((-3 + -4x)(1 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75Subproblem 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 = {-0.75, 0.5}
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