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Simplifying -24x2 + 78x + -33 = 0 Reorder the terms: -33 + 78x + -24x2 = 0 Solving -33 + 78x + -24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-11 + 26x + -8x2) = 0 Factor a trinomial. 3((-11 + 4x)(1 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-11 + 4x)' equal to zero and attempt to solve: Simplifying -11 + 4x = 0 Solving -11 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 4x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 4x = 0 + 11 4x = 0 + 11 Combine like terms: 0 + 11 = 11 4x = 11 Divide each side by '4'. x = 2.75 Simplifying x = 2.75Subproblem 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 = {2.75, 0.5}
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