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Simplifying (x + 4)(x + 4) = 2x2 + 9x + -14 Reorder the terms: (4 + x)(x + 4) = 2x2 + 9x + -14 Reorder the terms: (4 + x)(4 + x) = 2x2 + 9x + -14 Multiply (4 + x) * (4 + x) (4(4 + x) + x(4 + x)) = 2x2 + 9x + -14 ((4 * 4 + x * 4) + x(4 + x)) = 2x2 + 9x + -14 ((16 + 4x) + x(4 + x)) = 2x2 + 9x + -14 (16 + 4x + (4 * x + x * x)) = 2x2 + 9x + -14 (16 + 4x + (4x + x2)) = 2x2 + 9x + -14 Combine like terms: 4x + 4x = 8x (16 + 8x + x2) = 2x2 + 9x + -14 Reorder the terms: 16 + 8x + x2 = -14 + 9x + 2x2 Solving 16 + 8x + x2 = -14 + 9x + 2x2 Solving for variable 'x'. Reorder the terms: 16 + 14 + 8x + -9x + x2 + -2x2 = -14 + 9x + 2x2 + 14 + -9x + -2x2 Combine like terms: 16 + 14 = 30 30 + 8x + -9x + x2 + -2x2 = -14 + 9x + 2x2 + 14 + -9x + -2x2 Combine like terms: 8x + -9x = -1x 30 + -1x + x2 + -2x2 = -14 + 9x + 2x2 + 14 + -9x + -2x2 Combine like terms: x2 + -2x2 = -1x2 30 + -1x + -1x2 = -14 + 9x + 2x2 + 14 + -9x + -2x2 Reorder the terms: 30 + -1x + -1x2 = -14 + 14 + 9x + -9x + 2x2 + -2x2 Combine like terms: -14 + 14 = 0 30 + -1x + -1x2 = 0 + 9x + -9x + 2x2 + -2x2 30 + -1x + -1x2 = 9x + -9x + 2x2 + -2x2 Combine like terms: 9x + -9x = 0 30 + -1x + -1x2 = 0 + 2x2 + -2x2 30 + -1x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 30 + -1x + -1x2 = 0 Factor a trinomial. (5 + -1x)(6 + x) = 0Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {5, -6}
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