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Simplifying 20y2 = 2 + 6y Solving 20y2 = 2 + 6y Solving for variable 'y'. Reorder the terms: -2 + -6y + 20y2 = 2 + 6y + -2 + -6y Reorder the terms: -2 + -6y + 20y2 = 2 + -2 + 6y + -6y Combine like terms: 2 + -2 = 0 -2 + -6y + 20y2 = 0 + 6y + -6y -2 + -6y + 20y2 = 6y + -6y Combine like terms: 6y + -6y = 0 -2 + -6y + 20y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -3y + 10y2) = 0 Factor a trinomial. 2((-1 + -5y)(1 + -2y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -5y)' equal to zero and attempt to solve: Simplifying -1 + -5y = 0 Solving -1 + -5y = 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 + -5y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5y = 0 + 1 -5y = 0 + 1 Combine like terms: 0 + 1 = 1 -5y = 1 Divide each side by '-5'. y = -0.2 Simplifying y = -0.2Subproblem 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 = {-0.2, 0.5}
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