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Simplifying 9x2 = 51x + -30 Reorder the terms: 9x2 = -30 + 51x Solving 9x2 = -30 + 51x Solving for variable 'x'. Reorder the terms: 30 + -51x + 9x2 = -30 + 51x + 30 + -51x Reorder the terms: 30 + -51x + 9x2 = -30 + 30 + 51x + -51x Combine like terms: -30 + 30 = 0 30 + -51x + 9x2 = 0 + 51x + -51x 30 + -51x + 9x2 = 51x + -51x Combine like terms: 51x + -51x = 0 30 + -51x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(10 + -17x + 3x2) = 0 Factor a trinomial. 3((2 + -3x)(5 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Subproblem 2
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 = 5Solution
x = {0.6666666667, 5}
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