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Simplifying 2(x2 + 2x + -3) + -1(x2 + 3x) = 66 Reorder the terms: 2(-3 + 2x + x2) + -1(x2 + 3x) = 66 (-3 * 2 + 2x * 2 + x2 * 2) + -1(x2 + 3x) = 66 (-6 + 4x + 2x2) + -1(x2 + 3x) = 66 Reorder the terms: -6 + 4x + 2x2 + -1(3x + x2) = 66 -6 + 4x + 2x2 + (3x * -1 + x2 * -1) = 66 -6 + 4x + 2x2 + (-3x + -1x2) = 66 Reorder the terms: -6 + 4x + -3x + 2x2 + -1x2 = 66 Combine like terms: 4x + -3x = 1x -6 + 1x + 2x2 + -1x2 = 66 Combine like terms: 2x2 + -1x2 = 1x2 -6 + 1x + 1x2 = 66 Solving -6 + 1x + 1x2 = 66 Solving for variable 'x'. Reorder the terms: -6 + -66 + 1x + 1x2 = 66 + -66 Combine like terms: -6 + -66 = -72 -72 + 1x + 1x2 = 66 + -66 Combine like terms: 66 + -66 = 0 -72 + 1x + 1x2 = 0 Factor a trinomial. (-9 + -1x)(8 + -1x) = 0Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 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 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-9, 8}
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