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Simplifying y2 + -12y + 36 + y2 + 2y2 + -12y = 100 Reorder the terms: 36 + -12y + -12y + y2 + y2 + 2y2 = 100 Combine like terms: -12y + -12y = -24y 36 + -24y + y2 + y2 + 2y2 = 100 Combine like terms: y2 + y2 = 2y2 36 + -24y + 2y2 + 2y2 = 100 Combine like terms: 2y2 + 2y2 = 4y2 36 + -24y + 4y2 = 100 Solving 36 + -24y + 4y2 = 100 Solving for variable 'y'. Reorder the terms: 36 + -100 + -24y + 4y2 = 100 + -100 Combine like terms: 36 + -100 = -64 -64 + -24y + 4y2 = 100 + -100 Combine like terms: 100 + -100 = 0 -64 + -24y + 4y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-16 + -6y + y2) = 0 Factor a trinomial. 4((-2 + -1y)(8 + -1y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -1y)' equal to zero and attempt to solve: Simplifying -2 + -1y = 0 Solving -2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1y = 0 + 2 -1y = 0 + 2 Combine like terms: 0 + 2 = 2 -1y = 2 Divide each side by '-1'. y = -2 Simplifying y = -2Subproblem 2
Set the factor '(8 + -1y)' equal to zero and attempt to solve: Simplifying 8 + -1y = 0 Solving 8 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1y = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1y = 0 + -8 -1y = 0 + -8 Combine like terms: 0 + -8 = -8 -1y = -8 Divide each side by '-1'. y = 8 Simplifying y = 8Solution
y = {-2, 8}
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