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Simplifying 5x2 + -7x + 3 = 3x2 + -2x Reorder the terms: 3 + -7x + 5x2 = 3x2 + -2x Reorder the terms: 3 + -7x + 5x2 = -2x + 3x2 Solving 3 + -7x + 5x2 = -2x + 3x2 Solving for variable 'x'. Reorder the terms: 3 + -7x + 2x + 5x2 + -3x2 = -2x + 3x2 + 2x + -3x2 Combine like terms: -7x + 2x = -5x 3 + -5x + 5x2 + -3x2 = -2x + 3x2 + 2x + -3x2 Combine like terms: 5x2 + -3x2 = 2x2 3 + -5x + 2x2 = -2x + 3x2 + 2x + -3x2 Reorder the terms: 3 + -5x + 2x2 = -2x + 2x + 3x2 + -3x2 Combine like terms: -2x + 2x = 0 3 + -5x + 2x2 = 0 + 3x2 + -3x2 3 + -5x + 2x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 3 + -5x + 2x2 = 0 Factor a trinomial. (1 + -1x)(3 + -2x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {1, 1.5}
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