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Simplifying (25 + x)(15 + x) = 704 Multiply (25 + x) * (15 + x) (25(15 + x) + x(15 + x)) = 704 ((15 * 25 + x * 25) + x(15 + x)) = 704 ((375 + 25x) + x(15 + x)) = 704 (375 + 25x + (15 * x + x * x)) = 704 (375 + 25x + (15x + x2)) = 704 Combine like terms: 25x + 15x = 40x (375 + 40x + x2) = 704 Solving 375 + 40x + x2 = 704 Solving for variable 'x'. Reorder the terms: 375 + -704 + 40x + x2 = 704 + -704 Combine like terms: 375 + -704 = -329 -329 + 40x + x2 = 704 + -704 Combine like terms: 704 + -704 = 0 -329 + 40x + x2 = 0 Factor a trinomial. (-47 + -1x)(7 + -1x) = 0Subproblem 1
Set the factor '(-47 + -1x)' equal to zero and attempt to solve: Simplifying -47 + -1x = 0 Solving -47 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '47' to each side of the equation. -47 + 47 + -1x = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -1x = 0 + 47 -1x = 0 + 47 Combine like terms: 0 + 47 = 47 -1x = 47 Divide each side by '-1'. x = -47 Simplifying x = -47Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-47, 7}
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