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Simplifying x2 + 10x + 21 + x2 + -13x + -30 = x2 + -5x + -6 Reorder the terms: 21 + -30 + 10x + -13x + x2 + x2 = x2 + -5x + -6 Combine like terms: 21 + -30 = -9 -9 + 10x + -13x + x2 + x2 = x2 + -5x + -6 Combine like terms: 10x + -13x = -3x -9 + -3x + x2 + x2 = x2 + -5x + -6 Combine like terms: x2 + x2 = 2x2 -9 + -3x + 2x2 = x2 + -5x + -6 Reorder the terms: -9 + -3x + 2x2 = -6 + -5x + x2 Solving -9 + -3x + 2x2 = -6 + -5x + x2 Solving for variable 'x'. Reorder the terms: -9 + 6 + -3x + 5x + 2x2 + -1x2 = -6 + -5x + x2 + 6 + 5x + -1x2 Combine like terms: -9 + 6 = -3 -3 + -3x + 5x + 2x2 + -1x2 = -6 + -5x + x2 + 6 + 5x + -1x2 Combine like terms: -3x + 5x = 2x -3 + 2x + 2x2 + -1x2 = -6 + -5x + x2 + 6 + 5x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -3 + 2x + 1x2 = -6 + -5x + x2 + 6 + 5x + -1x2 Reorder the terms: -3 + 2x + 1x2 = -6 + 6 + -5x + 5x + x2 + -1x2 Combine like terms: -6 + 6 = 0 -3 + 2x + 1x2 = 0 + -5x + 5x + x2 + -1x2 -3 + 2x + 1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 -3 + 2x + 1x2 = 0 + x2 + -1x2 -3 + 2x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -3 + 2x + 1x2 = 0 Factor a trinomial. (-3 + -1x)(1 + -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 '(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 = 1Solution
x = {-3, 1}
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