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Simplifying 100 = y(21 + y) 100 = (21 * y + y * y) 100 = (21y + y2) Solving 100 = 21y + y2 Solving for variable 'y'. Reorder the terms: 100 + -21y + -1y2 = 21y + -21y + y2 + -1y2 Combine like terms: 21y + -21y = 0 100 + -21y + -1y2 = 0 + y2 + -1y2 100 + -21y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 100 + -21y + -1y2 = 0 Factor a trinomial. (4 + -1y)(25 + y) = 0Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4Subproblem 2
Set the factor '(25 + y)' equal to zero and attempt to solve: Simplifying 25 + y = 0 Solving 25 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + y = 0 + -25 Combine like terms: 25 + -25 = 0 0 + y = 0 + -25 y = 0 + -25 Combine like terms: 0 + -25 = -25 y = -25 Simplifying y = -25Solution
y = {4, -25}
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