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Simplifying 2x2 + 3x + -5 = 7x + 1 Reorder the terms: -5 + 3x + 2x2 = 7x + 1 Reorder the terms: -5 + 3x + 2x2 = 1 + 7x Solving -5 + 3x + 2x2 = 1 + 7x Solving for variable 'x'. Reorder the terms: -5 + -1 + 3x + -7x + 2x2 = 1 + 7x + -1 + -7x Combine like terms: -5 + -1 = -6 -6 + 3x + -7x + 2x2 = 1 + 7x + -1 + -7x Combine like terms: 3x + -7x = -4x -6 + -4x + 2x2 = 1 + 7x + -1 + -7x Reorder the terms: -6 + -4x + 2x2 = 1 + -1 + 7x + -7x Combine like terms: 1 + -1 = 0 -6 + -4x + 2x2 = 0 + 7x + -7x -6 + -4x + 2x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -6 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -2x + x2) = 0 Factor a trinomial. 2((-1 + -1x)(3 + -1x)) = 0 Ignore the factor 2.Subproblem 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 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-1, 3}
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