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Simplifying 252 = -16x2 + 90x + 288 Reorder the terms: 252 = 288 + 90x + -16x2 Solving 252 = 288 + 90x + -16x2 Solving for variable 'x'. Combine like terms: 252 + -288 = -36 -36 + -90x + 16x2 = 288 + 90x + -16x2 + -288 + -90x + 16x2 Reorder the terms: -36 + -90x + 16x2 = 288 + -288 + 90x + -90x + -16x2 + 16x2 Combine like terms: 288 + -288 = 0 -36 + -90x + 16x2 = 0 + 90x + -90x + -16x2 + 16x2 -36 + -90x + 16x2 = 90x + -90x + -16x2 + 16x2 Combine like terms: 90x + -90x = 0 -36 + -90x + 16x2 = 0 + -16x2 + 16x2 -36 + -90x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -36 + -90x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + -45x + 8x2) = 0 Factor a trinomial. 2((-3 + -8x)(6 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -8x)' equal to zero and attempt to solve: Simplifying -3 + -8x = 0 Solving -3 + -8x = 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 + -8x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8x = 0 + 3 -8x = 0 + 3 Combine like terms: 0 + 3 = 3 -8x = 3 Divide each side by '-8'. x = -0.375 Simplifying x = -0.375Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-0.375, 6}
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