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Simplifying 7(25 + -20y + 4y2) + 7 = 5y + -2y2 + 3y (25 * 7 + -20y * 7 + 4y2 * 7) + 7 = 5y + -2y2 + 3y (175 + -140y + 28y2) + 7 = 5y + -2y2 + 3y Reorder the terms: 175 + 7 + -140y + 28y2 = 5y + -2y2 + 3y Combine like terms: 175 + 7 = 182 182 + -140y + 28y2 = 5y + -2y2 + 3y Reorder the terms: 182 + -140y + 28y2 = 5y + 3y + -2y2 Combine like terms: 5y + 3y = 8y 182 + -140y + 28y2 = 8y + -2y2 Solving 182 + -140y + 28y2 = 8y + -2y2 Solving for variable 'y'. Reorder the terms: 182 + -140y + -8y + 28y2 + 2y2 = 8y + -2y2 + -8y + 2y2 Combine like terms: -140y + -8y = -148y 182 + -148y + 28y2 + 2y2 = 8y + -2y2 + -8y + 2y2 Combine like terms: 28y2 + 2y2 = 30y2 182 + -148y + 30y2 = 8y + -2y2 + -8y + 2y2 Reorder the terms: 182 + -148y + 30y2 = 8y + -8y + -2y2 + 2y2 Combine like terms: 8y + -8y = 0 182 + -148y + 30y2 = 0 + -2y2 + 2y2 182 + -148y + 30y2 = -2y2 + 2y2 Combine like terms: -2y2 + 2y2 = 0 182 + -148y + 30y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(91 + -74y + 15y2) = 0 Factor a trinomial. 2((7 + -3y)(13 + -5y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -3y)' equal to zero and attempt to solve: Simplifying 7 + -3y = 0 Solving 7 + -3y = 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 + -3y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3y = 0 + -7 -3y = 0 + -7 Combine like terms: 0 + -7 = -7 -3y = -7 Divide each side by '-3'. y = 2.333333333 Simplifying y = 2.333333333Subproblem 2
Set the factor '(13 + -5y)' equal to zero and attempt to solve: Simplifying 13 + -5y = 0 Solving 13 + -5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -5y = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -5y = 0 + -13 -5y = 0 + -13 Combine like terms: 0 + -13 = -13 -5y = -13 Divide each side by '-5'. y = 2.6 Simplifying y = 2.6Solution
y = {2.333333333, 2.6}
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