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Simplifying 0 = 9y2 + 42y + 49 Reorder the terms: 0 = 49 + 42y + 9y2 Solving 0 = 49 + 42y + 9y2 Solving for variable 'y'. Combine like terms: 0 + -49 = -49 -49 + -42y + -9y2 = 49 + 42y + 9y2 + -49 + -42y + -9y2 Reorder the terms: -49 + -42y + -9y2 = 49 + -49 + 42y + -42y + 9y2 + -9y2 Combine like terms: 49 + -49 = 0 -49 + -42y + -9y2 = 0 + 42y + -42y + 9y2 + -9y2 -49 + -42y + -9y2 = 42y + -42y + 9y2 + -9y2 Combine like terms: 42y + -42y = 0 -49 + -42y + -9y2 = 0 + 9y2 + -9y2 -49 + -42y + -9y2 = 9y2 + -9y2 Combine like terms: 9y2 + -9y2 = 0 -49 + -42y + -9y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(49 + 42y + 9y2) = 0 Factor a trinomial. -1((7 + 3y)(7 + 3y)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 3y)' equal to zero and attempt to solve: Simplifying 7 + 3y = 0 Solving 7 + 3y = 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 + 3y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3y = 0 + -7 3y = 0 + -7 Combine like terms: 0 + -7 = -7 3y = -7 Divide each side by '3'. y = -2.333333333 Simplifying y = -2.333333333Subproblem 2
Set the factor '(7 + 3y)' equal to zero and attempt to solve: Simplifying 7 + 3y = 0 Solving 7 + 3y = 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 + 3y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3y = 0 + -7 3y = 0 + -7 Combine like terms: 0 + -7 = -7 3y = -7 Divide each side by '3'. y = -2.333333333 Simplifying y = -2.333333333Solution
y = {-2.333333333, -2.333333333}
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