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Simplifying (x + 7)(x + 7) = 2x2 + 13x + 19 Reorder the terms: (7 + x)(x + 7) = 2x2 + 13x + 19 Reorder the terms: (7 + x)(7 + x) = 2x2 + 13x + 19 Multiply (7 + x) * (7 + x) (7(7 + x) + x(7 + x)) = 2x2 + 13x + 19 ((7 * 7 + x * 7) + x(7 + x)) = 2x2 + 13x + 19 ((49 + 7x) + x(7 + x)) = 2x2 + 13x + 19 (49 + 7x + (7 * x + x * x)) = 2x2 + 13x + 19 (49 + 7x + (7x + x2)) = 2x2 + 13x + 19 Combine like terms: 7x + 7x = 14x (49 + 14x + x2) = 2x2 + 13x + 19 Reorder the terms: 49 + 14x + x2 = 19 + 13x + 2x2 Solving 49 + 14x + x2 = 19 + 13x + 2x2 Solving for variable 'x'. Reorder the terms: 49 + -19 + 14x + -13x + x2 + -2x2 = 19 + 13x + 2x2 + -19 + -13x + -2x2 Combine like terms: 49 + -19 = 30 30 + 14x + -13x + x2 + -2x2 = 19 + 13x + 2x2 + -19 + -13x + -2x2 Combine like terms: 14x + -13x = 1x 30 + 1x + x2 + -2x2 = 19 + 13x + 2x2 + -19 + -13x + -2x2 Combine like terms: x2 + -2x2 = -1x2 30 + 1x + -1x2 = 19 + 13x + 2x2 + -19 + -13x + -2x2 Reorder the terms: 30 + 1x + -1x2 = 19 + -19 + 13x + -13x + 2x2 + -2x2 Combine like terms: 19 + -19 = 0 30 + 1x + -1x2 = 0 + 13x + -13x + 2x2 + -2x2 30 + 1x + -1x2 = 13x + -13x + 2x2 + -2x2 Combine like terms: 13x + -13x = 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. (6 + -1x)(5 + x) = 0Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 2
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 = -5Solution
x = {6, -5}
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