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Simplifying (30 + x)(20 + x) = 1064 Multiply (30 + x) * (20 + x) (30(20 + x) + x(20 + x)) = 1064 ((20 * 30 + x * 30) + x(20 + x)) = 1064 ((600 + 30x) + x(20 + x)) = 1064 (600 + 30x + (20 * x + x * x)) = 1064 (600 + 30x + (20x + x2)) = 1064 Combine like terms: 30x + 20x = 50x (600 + 50x + x2) = 1064 Solving 600 + 50x + x2 = 1064 Solving for variable 'x'. Reorder the terms: 600 + -1064 + 50x + x2 = 1064 + -1064 Combine like terms: 600 + -1064 = -464 -464 + 50x + x2 = 1064 + -1064 Combine like terms: 1064 + -1064 = 0 -464 + 50x + x2 = 0 Factor a trinomial. (-58 + -1x)(8 + -1x) = 0Subproblem 1
Set the factor '(-58 + -1x)' equal to zero and attempt to solve: Simplifying -58 + -1x = 0 Solving -58 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '58' to each side of the equation. -58 + 58 + -1x = 0 + 58 Combine like terms: -58 + 58 = 0 0 + -1x = 0 + 58 -1x = 0 + 58 Combine like terms: 0 + 58 = 58 -1x = 58 Divide each side by '-1'. x = -58 Simplifying x = -58Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-58, 8}
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