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Simplifying (x + 4)(x + 6) = 8 Reorder the terms: (4 + x)(x + 6) = 8 Reorder the terms: (4 + x)(6 + x) = 8 Multiply (4 + x) * (6 + x) (4(6 + x) + x(6 + x)) = 8 ((6 * 4 + x * 4) + x(6 + x)) = 8 ((24 + 4x) + x(6 + x)) = 8 (24 + 4x + (6 * x + x * x)) = 8 (24 + 4x + (6x + x2)) = 8 Combine like terms: 4x + 6x = 10x (24 + 10x + x2) = 8 Solving 24 + 10x + x2 = 8 Solving for variable 'x'. Reorder the terms: 24 + -8 + 10x + x2 = 8 + -8 Combine like terms: 24 + -8 = 16 16 + 10x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 16 + 10x + x2 = 0 Factor a trinomial. (8 + x)(2 + x) = 0Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 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 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-8, -2}
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