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Simplifying 28 = 180 + -54x + 4x2 Solving 28 = 180 + -54x + 4x2 Solving for variable 'x'. Combine like terms: 28 + -180 = -152 -152 + 54x + -4x2 = 180 + -54x + 4x2 + -180 + 54x + -4x2 Reorder the terms: -152 + 54x + -4x2 = 180 + -180 + -54x + 54x + 4x2 + -4x2 Combine like terms: 180 + -180 = 0 -152 + 54x + -4x2 = 0 + -54x + 54x + 4x2 + -4x2 -152 + 54x + -4x2 = -54x + 54x + 4x2 + -4x2 Combine like terms: -54x + 54x = 0 -152 + 54x + -4x2 = 0 + 4x2 + -4x2 -152 + 54x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -152 + 54x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-76 + 27x + -2x2) = 0 Factor a trinomial. 2((-19 + 2x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + 2x)' equal to zero and attempt to solve: Simplifying -19 + 2x = 0 Solving -19 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + 2x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 2x = 0 + 19 2x = 0 + 19 Combine like terms: 0 + 19 = 19 2x = 19 Divide each side by '2'. x = 9.5 Simplifying x = 9.5Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {9.5, 4}
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