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Simplifying 5y2 + 8y + -100 = y2 + 4y + -37 Reorder the terms: -100 + 8y + 5y2 = y2 + 4y + -37 Reorder the terms: -100 + 8y + 5y2 = -37 + 4y + y2 Solving -100 + 8y + 5y2 = -37 + 4y + y2 Solving for variable 'y'. Reorder the terms: -100 + 37 + 8y + -4y + 5y2 + -1y2 = -37 + 4y + y2 + 37 + -4y + -1y2 Combine like terms: -100 + 37 = -63 -63 + 8y + -4y + 5y2 + -1y2 = -37 + 4y + y2 + 37 + -4y + -1y2 Combine like terms: 8y + -4y = 4y -63 + 4y + 5y2 + -1y2 = -37 + 4y + y2 + 37 + -4y + -1y2 Combine like terms: 5y2 + -1y2 = 4y2 -63 + 4y + 4y2 = -37 + 4y + y2 + 37 + -4y + -1y2 Reorder the terms: -63 + 4y + 4y2 = -37 + 37 + 4y + -4y + y2 + -1y2 Combine like terms: -37 + 37 = 0 -63 + 4y + 4y2 = 0 + 4y + -4y + y2 + -1y2 -63 + 4y + 4y2 = 4y + -4y + y2 + -1y2 Combine like terms: 4y + -4y = 0 -63 + 4y + 4y2 = 0 + y2 + -1y2 -63 + 4y + 4y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -63 + 4y + 4y2 = 0 Factor a trinomial. (-9 + -2y)(7 + -2y) = 0Subproblem 1
Set the factor '(-9 + -2y)' equal to zero and attempt to solve: Simplifying -9 + -2y = 0 Solving -9 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2y = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2y = 0 + 9 -2y = 0 + 9 Combine like terms: 0 + 9 = 9 -2y = 9 Divide each side by '-2'. y = -4.5 Simplifying y = -4.5Subproblem 2
Set the factor '(7 + -2y)' equal to zero and attempt to solve: Simplifying 7 + -2y = 0 Solving 7 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2y = 0 + -7 -2y = 0 + -7 Combine like terms: 0 + -7 = -7 -2y = -7 Divide each side by '-2'. y = 3.5 Simplifying y = 3.5Solution
y = {-4.5, 3.5}
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