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Simplifying 5y2 + 80y + 400 = 2500 Reorder the terms: 400 + 80y + 5y2 = 2500 Solving 400 + 80y + 5y2 = 2500 Solving for variable 'y'. Reorder the terms: 400 + -2500 + 80y + 5y2 = 2500 + -2500 Combine like terms: 400 + -2500 = -2100 -2100 + 80y + 5y2 = 2500 + -2500 Combine like terms: 2500 + -2500 = 0 -2100 + 80y + 5y2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-420 + 16y + y2) = 0 Factor a trinomial. 5((-30 + -1y)(14 + -1y)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-30 + -1y)' equal to zero and attempt to solve: Simplifying -30 + -1y = 0 Solving -30 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + -1y = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -1y = 0 + 30 -1y = 0 + 30 Combine like terms: 0 + 30 = 30 -1y = 30 Divide each side by '-1'. y = -30 Simplifying y = -30Subproblem 2
Set the factor '(14 + -1y)' equal to zero and attempt to solve: Simplifying 14 + -1y = 0 Solving 14 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1y = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1y = 0 + -14 -1y = 0 + -14 Combine like terms: 0 + -14 = -14 -1y = -14 Divide each side by '-1'. y = 14 Simplifying y = 14Solution
y = {-30, 14}
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