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Simplifying 40 = (2x + 3)(x + 7) Reorder the terms: 40 = (3 + 2x)(x + 7) Reorder the terms: 40 = (3 + 2x)(7 + x) Multiply (3 + 2x) * (7 + x) 40 = (3(7 + x) + 2x * (7 + x)) 40 = ((7 * 3 + x * 3) + 2x * (7 + x)) 40 = ((21 + 3x) + 2x * (7 + x)) 40 = (21 + 3x + (7 * 2x + x * 2x)) 40 = (21 + 3x + (14x + 2x2)) Combine like terms: 3x + 14x = 17x 40 = (21 + 17x + 2x2) Solving 40 = 21 + 17x + 2x2 Solving for variable 'x'. Combine like terms: 40 + -21 = 19 19 + -17x + -2x2 = 21 + 17x + 2x2 + -21 + -17x + -2x2 Reorder the terms: 19 + -17x + -2x2 = 21 + -21 + 17x + -17x + 2x2 + -2x2 Combine like terms: 21 + -21 = 0 19 + -17x + -2x2 = 0 + 17x + -17x + 2x2 + -2x2 19 + -17x + -2x2 = 17x + -17x + 2x2 + -2x2 Combine like terms: 17x + -17x = 0 19 + -17x + -2x2 = 0 + 2x2 + -2x2 19 + -17x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 19 + -17x + -2x2 = 0 Factor a trinomial. (1 + -1x)(19 + 2x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(19 + 2x)' equal to zero and attempt to solve: Simplifying 19 + 2x = 0 Solving 19 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + 2x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 2x = 0 + -19 2x = 0 + -19 Combine like terms: 0 + -19 = -19 2x = -19 Divide each side by '2'. x = -9.5 Simplifying x = -9.5Solution
x = {1, -9.5}
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