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Simplifying 2x2 + 23x + 67 = (x + 7)(x + 7) Reorder the terms: 67 + 23x + 2x2 = (x + 7)(x + 7) Reorder the terms: 67 + 23x + 2x2 = (7 + x)(x + 7) Reorder the terms: 67 + 23x + 2x2 = (7 + x)(7 + x) Multiply (7 + x) * (7 + x) 67 + 23x + 2x2 = (7(7 + x) + x(7 + x)) 67 + 23x + 2x2 = ((7 * 7 + x * 7) + x(7 + x)) 67 + 23x + 2x2 = ((49 + 7x) + x(7 + x)) 67 + 23x + 2x2 = (49 + 7x + (7 * x + x * x)) 67 + 23x + 2x2 = (49 + 7x + (7x + x2)) Combine like terms: 7x + 7x = 14x 67 + 23x + 2x2 = (49 + 14x + x2) Solving 67 + 23x + 2x2 = 49 + 14x + x2 Solving for variable 'x'. Reorder the terms: 67 + -49 + 23x + -14x + 2x2 + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2 Combine like terms: 67 + -49 = 18 18 + 23x + -14x + 2x2 + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2 Combine like terms: 23x + -14x = 9x 18 + 9x + 2x2 + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 18 + 9x + 1x2 = 49 + 14x + x2 + -49 + -14x + -1x2 Reorder the terms: 18 + 9x + 1x2 = 49 + -49 + 14x + -14x + x2 + -1x2 Combine like terms: 49 + -49 = 0 18 + 9x + 1x2 = 0 + 14x + -14x + x2 + -1x2 18 + 9x + 1x2 = 14x + -14x + x2 + -1x2 Combine like terms: 14x + -14x = 0 18 + 9x + 1x2 = 0 + x2 + -1x2 18 + 9x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 18 + 9x + 1x2 = 0 Factor a trinomial. (6 + x)(3 + x) = 0Subproblem 1
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 = -6Subproblem 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 = {-6, -3}
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