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Simplifying 0 = 12y2 + 34y + 14 Reorder the terms: 0 = 14 + 34y + 12y2 Solving 0 = 14 + 34y + 12y2 Solving for variable 'y'. Combine like terms: 0 + -14 = -14 -14 + -34y + -12y2 = 14 + 34y + 12y2 + -14 + -34y + -12y2 Reorder the terms: -14 + -34y + -12y2 = 14 + -14 + 34y + -34y + 12y2 + -12y2 Combine like terms: 14 + -14 = 0 -14 + -34y + -12y2 = 0 + 34y + -34y + 12y2 + -12y2 -14 + -34y + -12y2 = 34y + -34y + 12y2 + -12y2 Combine like terms: 34y + -34y = 0 -14 + -34y + -12y2 = 0 + 12y2 + -12y2 -14 + -34y + -12y2 = 12y2 + -12y2 Combine like terms: 12y2 + -12y2 = 0 -14 + -34y + -12y2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(7 + 17y + 6y2) = 0 Factor a trinomial. -2((7 + 3y)(1 + 2y)) = 0 Ignore the factor -2.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 '(1 + 2y)' equal to zero and attempt to solve: Simplifying 1 + 2y = 0 Solving 1 + 2y = 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 + 2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2y = 0 + -1 2y = 0 + -1 Combine like terms: 0 + -1 = -1 2y = -1 Divide each side by '2'. y = -0.5 Simplifying y = -0.5Solution
y = {-2.333333333, -0.5}
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