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Simplifying 6x2 + 9x + -3 = 102 Reorder the terms: -3 + 9x + 6x2 = 102 Solving -3 + 9x + 6x2 = 102 Solving for variable 'x'. Reorder the terms: -3 + -102 + 9x + 6x2 = 102 + -102 Combine like terms: -3 + -102 = -105 -105 + 9x + 6x2 = 102 + -102 Combine like terms: 102 + -102 = 0 -105 + 9x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-35 + 3x + 2x2) = 0 Factor a trinomial. 3((-5 + -1x)(7 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 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 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5Solution
x = {-5, 3.5}
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