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Simplifying (2x2 + 2x + -5) + -1(x2 + 3x + 7) = 0 Reorder the terms: (-5 + 2x + 2x2) + -1(x2 + 3x + 7) = 0 Remove parenthesis around (-5 + 2x + 2x2) -5 + 2x + 2x2 + -1(x2 + 3x + 7) = 0 Reorder the terms: -5 + 2x + 2x2 + -1(7 + 3x + x2) = 0 -5 + 2x + 2x2 + (7 * -1 + 3x * -1 + x2 * -1) = 0 -5 + 2x + 2x2 + (-7 + -3x + -1x2) = 0 Reorder the terms: -5 + -7 + 2x + -3x + 2x2 + -1x2 = 0 Combine like terms: -5 + -7 = -12 -12 + 2x + -3x + 2x2 + -1x2 = 0 Combine like terms: 2x + -3x = -1x -12 + -1x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 -12 + -1x + 1x2 = 0 Solving -12 + -1x + 1x2 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + -1x)(4 + -1x) = 0Subproblem 1
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 = -3Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-3, 4}
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