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Simplifying (x + 2)(x + -2) + -7(x + -1) = 21 Reorder the terms: (2 + x)(x + -2) + -7(x + -1) = 21 Reorder the terms: (2 + x)(-2 + x) + -7(x + -1) = 21 Multiply (2 + x) * (-2 + x) (2(-2 + x) + x(-2 + x)) + -7(x + -1) = 21 ((-2 * 2 + x * 2) + x(-2 + x)) + -7(x + -1) = 21 ((-4 + 2x) + x(-2 + x)) + -7(x + -1) = 21 (-4 + 2x + (-2 * x + x * x)) + -7(x + -1) = 21 (-4 + 2x + (-2x + x2)) + -7(x + -1) = 21 Combine like terms: 2x + -2x = 0 (-4 + 0 + x2) + -7(x + -1) = 21 (-4 + x2) + -7(x + -1) = 21 Reorder the terms: -4 + x2 + -7(-1 + x) = 21 -4 + x2 + (-1 * -7 + x * -7) = 21 -4 + x2 + (7 + -7x) = 21 Reorder the terms: -4 + 7 + -7x + x2 = 21 Combine like terms: -4 + 7 = 3 3 + -7x + x2 = 21 Solving 3 + -7x + x2 = 21 Solving for variable 'x'. Reorder the terms: 3 + -21 + -7x + x2 = 21 + -21 Combine like terms: 3 + -21 = -18 -18 + -7x + x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -18 + -7x + x2 = 0 Factor a trinomial. (-2 + -1x)(9 + -1x) = 0Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
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 = 9Solution
x = {-2, 9}
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