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Simplifying 0 = 4y2 + 14y + 10 Reorder the terms: 0 = 10 + 14y + 4y2 Solving 0 = 10 + 14y + 4y2 Solving for variable 'y'. Combine like terms: 0 + -10 = -10 -10 + -14y + -4y2 = 10 + 14y + 4y2 + -10 + -14y + -4y2 Reorder the terms: -10 + -14y + -4y2 = 10 + -10 + 14y + -14y + 4y2 + -4y2 Combine like terms: 10 + -10 = 0 -10 + -14y + -4y2 = 0 + 14y + -14y + 4y2 + -4y2 -10 + -14y + -4y2 = 14y + -14y + 4y2 + -4y2 Combine like terms: 14y + -14y = 0 -10 + -14y + -4y2 = 0 + 4y2 + -4y2 -10 + -14y + -4y2 = 4y2 + -4y2 Combine like terms: 4y2 + -4y2 = 0 -10 + -14y + -4y2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + 7y + 2y2) = 0 Factor a trinomial. -2((5 + 2y)(1 + y)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + 2y)' equal to zero and attempt to solve: Simplifying 5 + 2y = 0 Solving 5 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2y = 0 + -5 2y = 0 + -5 Combine like terms: 0 + -5 = -5 2y = -5 Divide each side by '2'. y = -2.5 Simplifying y = -2.5Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve: Simplifying 1 + y = 0 Solving 1 + y = 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 + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0 + -1 y = 0 + -1 Combine like terms: 0 + -1 = -1 y = -1 Simplifying y = -1Solution
y = {-2.5, -1}
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