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Simplifying (x + 8)(x + -2) + 21 = 0 Reorder the terms: (8 + x)(x + -2) + 21 = 0 Reorder the terms: (8 + x)(-2 + x) + 21 = 0 Multiply (8 + x) * (-2 + x) (8(-2 + x) + x(-2 + x)) + 21 = 0 ((-2 * 8 + x * 8) + x(-2 + x)) + 21 = 0 ((-16 + 8x) + x(-2 + x)) + 21 = 0 (-16 + 8x + (-2 * x + x * x)) + 21 = 0 (-16 + 8x + (-2x + x2)) + 21 = 0 Combine like terms: 8x + -2x = 6x (-16 + 6x + x2) + 21 = 0 Reorder the terms: -16 + 21 + 6x + x2 = 0 Combine like terms: -16 + 21 = 5 5 + 6x + x2 = 0 Solving 5 + 6x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (5 + x)(1 + x) = 0Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-5, -1}
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