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Simplifying (y + -5)(y + -5) = 16 Reorder the terms: (-5 + y)(y + -5) = 16 Reorder the terms: (-5 + y)(-5 + y) = 16 Multiply (-5 + y) * (-5 + y) (-5(-5 + y) + y(-5 + y)) = 16 ((-5 * -5 + y * -5) + y(-5 + y)) = 16 ((25 + -5y) + y(-5 + y)) = 16 (25 + -5y + (-5 * y + y * y)) = 16 (25 + -5y + (-5y + y2)) = 16 Combine like terms: -5y + -5y = -10y (25 + -10y + y2) = 16 Solving 25 + -10y + y2 = 16 Solving for variable 'y'. Reorder the terms: 25 + -16 + -10y + y2 = 16 + -16 Combine like terms: 25 + -16 = 9 9 + -10y + y2 = 16 + -16 Combine like terms: 16 + -16 = 0 9 + -10y + y2 = 0 Factor a trinomial. (1 + -1y)(9 + -1y) = 0Subproblem 1
Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1Subproblem 2
Set the factor '(9 + -1y)' equal to zero and attempt to solve: Simplifying 9 + -1y = 0 Solving 9 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1y = 0 + -9 -1y = 0 + -9 Combine like terms: 0 + -9 = -9 -1y = -9 Divide each side by '-1'. y = 9 Simplifying y = 9Solution
y = {1, 9}
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