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Simplifying 7x2 + -3x = x2 + -20x + 45 Reorder the terms: -3x + 7x2 = x2 + -20x + 45 Reorder the terms: -3x + 7x2 = 45 + -20x + x2 Solving -3x + 7x2 = 45 + -20x + x2 Solving for variable 'x'. Reorder the terms: -45 + -3x + 20x + 7x2 + -1x2 = 45 + -20x + x2 + -45 + 20x + -1x2 Combine like terms: -3x + 20x = 17x -45 + 17x + 7x2 + -1x2 = 45 + -20x + x2 + -45 + 20x + -1x2 Combine like terms: 7x2 + -1x2 = 6x2 -45 + 17x + 6x2 = 45 + -20x + x2 + -45 + 20x + -1x2 Reorder the terms: -45 + 17x + 6x2 = 45 + -45 + -20x + 20x + x2 + -1x2 Combine like terms: 45 + -45 = 0 -45 + 17x + 6x2 = 0 + -20x + 20x + x2 + -1x2 -45 + 17x + 6x2 = -20x + 20x + x2 + -1x2 Combine like terms: -20x + 20x = 0 -45 + 17x + 6x2 = 0 + x2 + -1x2 -45 + 17x + 6x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -45 + 17x + 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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