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Simplifying 0 = 6x2 + -37x + 45 Reorder the terms: 0 = 45 + -37x + 6x2 Solving 0 = 45 + -37x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -45 = -45 -45 + 37x + -6x2 = 45 + -37x + 6x2 + -45 + 37x + -6x2 Reorder the terms: -45 + 37x + -6x2 = 45 + -45 + -37x + 37x + 6x2 + -6x2 Combine like terms: 45 + -45 = 0 -45 + 37x + -6x2 = 0 + -37x + 37x + 6x2 + -6x2 -45 + 37x + -6x2 = -37x + 37x + 6x2 + -6x2 Combine like terms: -37x + 37x = 0 -45 + 37x + -6x2 = 0 + 6x2 + -6x2 -45 + 37x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -45 + 37x + -6x2 = 0 Factor a trinomial. (-9 + 2x)(5 + -3x) = 0Subproblem 1
Set the factor '(-9 + 2x)' equal to zero and attempt to solve: Simplifying -9 + 2x = 0 Solving -9 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x = 0 + 9 2x = 0 + 9 Combine like terms: 0 + 9 = 9 2x = 9 Divide each side by '2'. x = 4.5 Simplifying x = 4.5Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667Solution
x = {4.5, 1.666666667}
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