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Simplifying (x + 7)(2x + 5) = 56 Reorder the terms: (7 + x)(2x + 5) = 56 Reorder the terms: (7 + x)(5 + 2x) = 56 Multiply (7 + x) * (5 + 2x) (7(5 + 2x) + x(5 + 2x)) = 56 ((5 * 7 + 2x * 7) + x(5 + 2x)) = 56 ((35 + 14x) + x(5 + 2x)) = 56 (35 + 14x + (5 * x + 2x * x)) = 56 (35 + 14x + (5x + 2x2)) = 56 Combine like terms: 14x + 5x = 19x (35 + 19x + 2x2) = 56 Solving 35 + 19x + 2x2 = 56 Solving for variable 'x'. Reorder the terms: 35 + -56 + 19x + 2x2 = 56 + -56 Combine like terms: 35 + -56 = -21 -21 + 19x + 2x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -21 + 19x + 2x2 = 0 Factor a trinomial. (-21 + -2x)(1 + -1x) = 0Subproblem 1
Set the factor '(-21 + -2x)' equal to zero and attempt to solve: Simplifying -21 + -2x = 0 Solving -21 + -2x = 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 + -2x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -2x = 0 + 21 -2x = 0 + 21 Combine like terms: 0 + 21 = 21 -2x = 21 Divide each side by '-2'. x = -10.5 Simplifying x = -10.5Subproblem 2
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 = 1Solution
x = {-10.5, 1}
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