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Simplifying 10y2 = 25 + 15y Solving 10y2 = 25 + 15y Solving for variable 'y'. Reorder the terms: -25 + -15y + 10y2 = 25 + 15y + -25 + -15y Reorder the terms: -25 + -15y + 10y2 = 25 + -25 + 15y + -15y Combine like terms: 25 + -25 = 0 -25 + -15y + 10y2 = 0 + 15y + -15y -25 + -15y + 10y2 = 15y + -15y Combine like terms: 15y + -15y = 0 -25 + -15y + 10y2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-5 + -3y + 2y2) = 0 Factor a trinomial. 5((-1 + -1y)(5 + -2y)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + -1y)' equal to zero and attempt to solve: Simplifying -1 + -1y = 0 Solving -1 + -1y = 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 + -1y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1y = 0 + 1 -1y = 0 + 1 Combine like terms: 0 + 1 = 1 -1y = 1 Divide each side by '-1'. y = -1 Simplifying y = -1Subproblem 2
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 = 2.5Solution
y = {-1, 2.5}
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