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Simplifying (x + 2)(x + 4) + 1 = 0 Reorder the terms: (2 + x)(x + 4) + 1 = 0 Reorder the terms: (2 + x)(4 + x) + 1 = 0 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) + 1 = 0 ((4 * 2 + x * 2) + x(4 + x)) + 1 = 0 ((8 + 2x) + x(4 + x)) + 1 = 0 (8 + 2x + (4 * x + x * x)) + 1 = 0 (8 + 2x + (4x + x2)) + 1 = 0 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) + 1 = 0 Reorder the terms: 8 + 1 + 6x + x2 = 0 Combine like terms: 8 + 1 = 9 9 + 6x + x2 = 0 Solving 9 + 6x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + x)(3 + x) = 0Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {-3, -3}
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