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Simplifying 0 = 18x2 + -96x + 126 Reorder the terms: 0 = 126 + -96x + 18x2 Solving 0 = 126 + -96x + 18x2 Solving for variable 'x'. Combine like terms: 0 + -126 = -126 -126 + 96x + -18x2 = 126 + -96x + 18x2 + -126 + 96x + -18x2 Reorder the terms: -126 + 96x + -18x2 = 126 + -126 + -96x + 96x + 18x2 + -18x2 Combine like terms: 126 + -126 = 0 -126 + 96x + -18x2 = 0 + -96x + 96x + 18x2 + -18x2 -126 + 96x + -18x2 = -96x + 96x + 18x2 + -18x2 Combine like terms: -96x + 96x = 0 -126 + 96x + -18x2 = 0 + 18x2 + -18x2 -126 + 96x + -18x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -126 + 96x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-21 + 16x + -3x2) = 0 Factor a trinomial. 6((-3 + x)(7 + -3x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Divide each side by '-3'. x = 2.333333333 Simplifying x = 2.333333333Solution
x = {3, 2.333333333}
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