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Simplifying (16 + x)(30 + x) = 1632 Multiply (16 + x) * (30 + x) (16(30 + x) + x(30 + x)) = 1632 ((30 * 16 + x * 16) + x(30 + x)) = 1632 ((480 + 16x) + x(30 + x)) = 1632 (480 + 16x + (30 * x + x * x)) = 1632 (480 + 16x + (30x + x2)) = 1632 Combine like terms: 16x + 30x = 46x (480 + 46x + x2) = 1632 Solving 480 + 46x + x2 = 1632 Solving for variable 'x'. Reorder the terms: 480 + -1632 + 46x + x2 = 1632 + -1632 Combine like terms: 480 + -1632 = -1152 -1152 + 46x + x2 = 1632 + -1632 Combine like terms: 1632 + -1632 = 0 -1152 + 46x + x2 = 0 Factor a trinomial. (-64 + -1x)(18 + -1x) = 0Subproblem 1
Set the factor '(-64 + -1x)' equal to zero and attempt to solve: Simplifying -64 + -1x = 0 Solving -64 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '64' to each side of the equation. -64 + 64 + -1x = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -1x = 0 + 64 -1x = 0 + 64 Combine like terms: 0 + 64 = 64 -1x = 64 Divide each side by '-1'. x = -64 Simplifying x = -64Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve: Simplifying 18 + -1x = 0 Solving 18 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1x = 0 + -18 -1x = 0 + -18 Combine like terms: 0 + -18 = -18 -1x = -18 Divide each side by '-1'. x = 18 Simplifying x = 18Solution
x = {-64, 18}
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