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Simplifying 2y2 + 11y + 21 = (y + 7)(y + 7) Reorder the terms: 21 + 11y + 2y2 = (y + 7)(y + 7) Reorder the terms: 21 + 11y + 2y2 = (7 + y)(y + 7) Reorder the terms: 21 + 11y + 2y2 = (7 + y)(7 + y) Multiply (7 + y) * (7 + y) 21 + 11y + 2y2 = (7(7 + y) + y(7 + y)) 21 + 11y + 2y2 = ((7 * 7 + y * 7) + y(7 + y)) 21 + 11y + 2y2 = ((49 + 7y) + y(7 + y)) 21 + 11y + 2y2 = (49 + 7y + (7 * y + y * y)) 21 + 11y + 2y2 = (49 + 7y + (7y + y2)) Combine like terms: 7y + 7y = 14y 21 + 11y + 2y2 = (49 + 14y + y2) Solving 21 + 11y + 2y2 = 49 + 14y + y2 Solving for variable 'y'. Reorder the terms: 21 + -49 + 11y + -14y + 2y2 + -1y2 = 49 + 14y + y2 + -49 + -14y + -1y2 Combine like terms: 21 + -49 = -28 -28 + 11y + -14y + 2y2 + -1y2 = 49 + 14y + y2 + -49 + -14y + -1y2 Combine like terms: 11y + -14y = -3y -28 + -3y + 2y2 + -1y2 = 49 + 14y + y2 + -49 + -14y + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 -28 + -3y + 1y2 = 49 + 14y + y2 + -49 + -14y + -1y2 Reorder the terms: -28 + -3y + 1y2 = 49 + -49 + 14y + -14y + y2 + -1y2 Combine like terms: 49 + -49 = 0 -28 + -3y + 1y2 = 0 + 14y + -14y + y2 + -1y2 -28 + -3y + 1y2 = 14y + -14y + y2 + -1y2 Combine like terms: 14y + -14y = 0 -28 + -3y + 1y2 = 0 + y2 + -1y2 -28 + -3y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -28 + -3y + 1y2 = 0 Factor a trinomial. (-4 + -1y)(7 + -1y) = 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 '(7 + -1y)' equal to zero and attempt to solve: Simplifying 7 + -1y = 0 Solving 7 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1y = 0 + -7 -1y = 0 + -7 Combine like terms: 0 + -7 = -7 -1y = -7 Divide each side by '-1'. y = 7 Simplifying y = 7Solution
y = {-4, 7}
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