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Simplifying 126 = (7 + x)(12 + x) Multiply (7 + x) * (12 + x) 126 = (7(12 + x) + x(12 + x)) 126 = ((12 * 7 + x * 7) + x(12 + x)) 126 = ((84 + 7x) + x(12 + x)) 126 = (84 + 7x + (12 * x + x * x)) 126 = (84 + 7x + (12x + x2)) Combine like terms: 7x + 12x = 19x 126 = (84 + 19x + x2) Solving 126 = 84 + 19x + x2 Solving for variable 'x'. Combine like terms: 126 + -84 = 42 42 + -19x + -1x2 = 84 + 19x + x2 + -84 + -19x + -1x2 Reorder the terms: 42 + -19x + -1x2 = 84 + -84 + 19x + -19x + x2 + -1x2 Combine like terms: 84 + -84 = 0 42 + -19x + -1x2 = 0 + 19x + -19x + x2 + -1x2 42 + -19x + -1x2 = 19x + -19x + x2 + -1x2 Combine like terms: 19x + -19x = 0 42 + -19x + -1x2 = 0 + x2 + -1x2 42 + -19x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 42 + -19x + -1x2 = 0 Factor a trinomial. (2 + -1x)(21 + x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(21 + x)' equal to zero and attempt to solve: Simplifying 21 + x = 0 Solving 21 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + x = 0 + -21 x = 0 + -21 Combine like terms: 0 + -21 = -21 x = -21 Simplifying x = -21Solution
x = {2, -21}
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