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Simplifying 2y(y + 4) + 3(y + -4) = 0 Reorder the terms: 2y(4 + y) + 3(y + -4) = 0 (4 * 2y + y * 2y) + 3(y + -4) = 0 (8y + 2y2) + 3(y + -4) = 0 Reorder the terms: 8y + 2y2 + 3(-4 + y) = 0 8y + 2y2 + (-4 * 3 + y * 3) = 0 8y + 2y2 + (-12 + 3y) = 0 Reorder the terms: -12 + 8y + 3y + 2y2 = 0 Combine like terms: 8y + 3y = 11y -12 + 11y + 2y2 = 0 Solving -12 + 11y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + 5.5y + y2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 5.5y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + 5.5y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 5.5y + y2 = 0 + 6 5.5y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 5.5y + y2 = 6 The y term is 5.5y. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5y + 7.5625 + y2 = 6 + 7.5625 Reorder the terms: 7.5625 + 5.5y + y2 = 6 + 7.5625 Combine like terms: 6 + 7.5625 = 13.5625 7.5625 + 5.5y + y2 = 13.5625 Factor a perfect square on the left side: (y + 2.75)(y + 2.75) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (y + 2.75) equal to 3.682729966 and -3.682729966.Subproblem 1
y + 2.75 = 3.682729966 Simplifying y + 2.75 = 3.682729966 Reorder the terms: 2.75 + y = 3.682729966 Solving 2.75 + y = 3.682729966 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + y = 3.682729966 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + y = 3.682729966 + -2.75 y = 3.682729966 + -2.75 Combine like terms: 3.682729966 + -2.75 = 0.932729966 y = 0.932729966 Simplifying y = 0.932729966Subproblem 2
y + 2.75 = -3.682729966 Simplifying y + 2.75 = -3.682729966 Reorder the terms: 2.75 + y = -3.682729966 Solving 2.75 + y = -3.682729966 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + y = -3.682729966 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + y = -3.682729966 + -2.75 y = -3.682729966 + -2.75 Combine like terms: -3.682729966 + -2.75 = -6.432729966 y = -6.432729966 Simplifying y = -6.432729966Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.932729966, -6.432729966}
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