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Simplifying 10y2 = 5 + -23y Solving 10y2 = 5 + -23y Solving for variable 'y'. Reorder the terms: -5 + 23y + 10y2 = 5 + -23y + -5 + 23y Reorder the terms: -5 + 23y + 10y2 = 5 + -5 + -23y + 23y Combine like terms: 5 + -5 = 0 -5 + 23y + 10y2 = 0 + -23y + 23y -5 + 23y + 10y2 = -23y + 23y Combine like terms: -23y + 23y = 0 -5 + 23y + 10y2 = 0 Factor a trinomial. (-5 + -2y)(1 + -5y) = 0Subproblem 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 + -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 = 0.2Solution
y = {-2.5, 0.2}
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