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Simplifying 400 = y(30 + y) 400 = (30 * y + y * y) 400 = (30y + y2) Solving 400 = 30y + y2 Solving for variable 'y'. Reorder the terms: 400 + -30y + -1y2 = 30y + -30y + y2 + -1y2 Combine like terms: 30y + -30y = 0 400 + -30y + -1y2 = 0 + y2 + -1y2 400 + -30y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 400 + -30y + -1y2 = 0 Factor a trinomial. (10 + -1y)(40 + y) = 0Subproblem 1
Set the factor '(10 + -1y)' equal to zero and attempt to solve: Simplifying 10 + -1y = 0 Solving 10 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1y = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1y = 0 + -10 -1y = 0 + -10 Combine like terms: 0 + -10 = -10 -1y = -10 Divide each side by '-1'. y = 10 Simplifying y = 10Subproblem 2
Set the factor '(40 + y)' equal to zero and attempt to solve: Simplifying 40 + y = 0 Solving 40 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + y = 0 + -40 Combine like terms: 40 + -40 = 0 0 + y = 0 + -40 y = 0 + -40 Combine like terms: 0 + -40 = -40 y = -40 Simplifying y = -40Solution
y = {10, -40}
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