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Simplifying (50 + y)(50 + y) = 16900 Multiply (50 + y) * (50 + y) (50(50 + y) + y(50 + y)) = 16900 ((50 * 50 + y * 50) + y(50 + y)) = 16900 ((2500 + 50y) + y(50 + y)) = 16900 (2500 + 50y + (50 * y + y * y)) = 16900 (2500 + 50y + (50y + y2)) = 16900 Combine like terms: 50y + 50y = 100y (2500 + 100y + y2) = 16900 Solving 2500 + 100y + y2 = 16900 Solving for variable 'y'. Reorder the terms: 2500 + -16900 + 100y + y2 = 16900 + -16900 Combine like terms: 2500 + -16900 = -14400 -14400 + 100y + y2 = 16900 + -16900 Combine like terms: 16900 + -16900 = 0 -14400 + 100y + y2 = 0 Factor a trinomial. (-180 + -1y)(80 + -1y) = 0Subproblem 1
Set the factor '(-180 + -1y)' equal to zero and attempt to solve: Simplifying -180 + -1y = 0 Solving -180 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '180' to each side of the equation. -180 + 180 + -1y = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -1y = 0 + 180 -1y = 0 + 180 Combine like terms: 0 + 180 = 180 -1y = 180 Divide each side by '-1'. y = -180 Simplifying y = -180Subproblem 2
Set the factor '(80 + -1y)' equal to zero and attempt to solve: Simplifying 80 + -1y = 0 Solving 80 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + -1y = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -1y = 0 + -80 -1y = 0 + -80 Combine like terms: 0 + -80 = -80 -1y = -80 Divide each side by '-1'. y = 80 Simplifying y = 80Solution
y = {-180, 80}
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