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Simplifying 100 = y2 + 4y + 40 Reorder the terms: 100 = 40 + 4y + y2 Solving 100 = 40 + 4y + y2 Solving for variable 'y'. Combine like terms: 100 + -40 = 60 60 + -4y + -1y2 = 40 + 4y + y2 + -40 + -4y + -1y2 Reorder the terms: 60 + -4y + -1y2 = 40 + -40 + 4y + -4y + y2 + -1y2 Combine like terms: 40 + -40 = 0 60 + -4y + -1y2 = 0 + 4y + -4y + y2 + -1y2 60 + -4y + -1y2 = 4y + -4y + y2 + -1y2 Combine like terms: 4y + -4y = 0 60 + -4y + -1y2 = 0 + y2 + -1y2 60 + -4y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 60 + -4y + -1y2 = 0 Factor a trinomial. (6 + -1y)(10 + y) = 0Subproblem 1
Set the factor '(6 + -1y)' equal to zero and attempt to solve: Simplifying 6 + -1y = 0 Solving 6 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1y = 0 + -6 -1y = 0 + -6 Combine like terms: 0 + -6 = -6 -1y = -6 Divide each side by '-1'. y = 6 Simplifying y = 6Subproblem 2
Set the factor '(10 + y)' equal to zero and attempt to solve: Simplifying 10 + y = 0 Solving 10 + y = 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 + y = 0 + -10 Combine like terms: 10 + -10 = 0 0 + y = 0 + -10 y = 0 + -10 Combine like terms: 0 + -10 = -10 y = -10 Simplifying y = -10Solution
y = {6, -10}
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