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Simplifying (2y + 7)(2y + 7) = 49 Reorder the terms: (7 + 2y)(2y + 7) = 49 Reorder the terms: (7 + 2y)(7 + 2y) = 49 Multiply (7 + 2y) * (7 + 2y) (7(7 + 2y) + 2y * (7 + 2y)) = 49 ((7 * 7 + 2y * 7) + 2y * (7 + 2y)) = 49 ((49 + 14y) + 2y * (7 + 2y)) = 49 (49 + 14y + (7 * 2y + 2y * 2y)) = 49 (49 + 14y + (14y + 4y2)) = 49 Combine like terms: 14y + 14y = 28y (49 + 28y + 4y2) = 49 Add '-49' to each side of the equation. 49 + 28y + -49 + 4y2 = 49 + -49 Reorder the terms: 49 + -49 + 28y + 4y2 = 49 + -49 Combine like terms: 49 + -49 = 0 0 + 28y + 4y2 = 49 + -49 28y + 4y2 = 49 + -49 Combine like terms: 49 + -49 = 0 28y + 4y2 = 0 Solving 28y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4y'. 4y(7 + y) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(7 + y)' equal to zero and attempt to solve: Simplifying 7 + y = 0 Solving 7 + y = 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 + y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + y = 0 + -7 y = 0 + -7 Combine like terms: 0 + -7 = -7 y = -7 Simplifying y = -7Solution
y = {0, -7}
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