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Simplifying 0 = 4Y2 + 84Y + 441 Reorder the terms: 0 = 441 + 84Y + 4Y2 Solving 0 = 441 + 84Y + 4Y2 Solving for variable 'Y'. Combine like terms: 0 + -441 = -441 -441 + -84Y + -4Y2 = 441 + 84Y + 4Y2 + -441 + -84Y + -4Y2 Reorder the terms: -441 + -84Y + -4Y2 = 441 + -441 + 84Y + -84Y + 4Y2 + -4Y2 Combine like terms: 441 + -441 = 0 -441 + -84Y + -4Y2 = 0 + 84Y + -84Y + 4Y2 + -4Y2 -441 + -84Y + -4Y2 = 84Y + -84Y + 4Y2 + -4Y2 Combine like terms: 84Y + -84Y = 0 -441 + -84Y + -4Y2 = 0 + 4Y2 + -4Y2 -441 + -84Y + -4Y2 = 4Y2 + -4Y2 Combine like terms: 4Y2 + -4Y2 = 0 -441 + -84Y + -4Y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(441 + 84Y + 4Y2) = 0 Factor a trinomial. -1((21 + 2Y)(21 + 2Y)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(21 + 2Y)' equal to zero and attempt to solve: Simplifying 21 + 2Y = 0 Solving 21 + 2Y = 0 Move all terms containing Y to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + 2Y = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 2Y = 0 + -21 2Y = 0 + -21 Combine like terms: 0 + -21 = -21 2Y = -21 Divide each side by '2'. Y = -10.5 Simplifying Y = -10.5Subproblem 2
Set the factor '(21 + 2Y)' equal to zero and attempt to solve: Simplifying 21 + 2Y = 0 Solving 21 + 2Y = 0 Move all terms containing Y to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + 2Y = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 2Y = 0 + -21 2Y = 0 + -21 Combine like terms: 0 + -21 = -21 2Y = -21 Divide each side by '2'. Y = -10.5 Simplifying Y = -10.5Solution
Y = {-10.5, -10.5}
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