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Simplifying 2y(y + 4) = 85 Reorder the terms: 2y(4 + y) = 85 (4 * 2y + y * 2y) = 85 (8y + 2y2) = 85 Solving 8y + 2y2 = 85 Solving for variable 'y'. Reorder the terms: -85 + 8y + 2y2 = 85 + -85 Combine like terms: 85 + -85 = 0 -85 + 8y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -42.5 + 4y + y2 = 0 Move the constant term to the right: Add '42.5' to each side of the equation. -42.5 + 4y + 42.5 + y2 = 0 + 42.5 Reorder the terms: -42.5 + 42.5 + 4y + y2 = 0 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + 4y + y2 = 0 + 42.5 4y + y2 = 0 + 42.5 Combine like terms: 0 + 42.5 = 42.5 4y + y2 = 42.5 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 42.5 + 4 Reorder the terms: 4 + 4y + y2 = 42.5 + 4 Combine like terms: 42.5 + 4 = 46.5 4 + 4y + y2 = 46.5 Factor a perfect square on the left side: (y + 2)(y + 2) = 46.5 Calculate the square root of the right side: 6.819090848 Break this problem into two subproblems by setting (y + 2) equal to 6.819090848 and -6.819090848.Subproblem 1
y + 2 = 6.819090848 Simplifying y + 2 = 6.819090848 Reorder the terms: 2 + y = 6.819090848 Solving 2 + y = 6.819090848 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 6.819090848 + -2 Combine like terms: 2 + -2 = 0 0 + y = 6.819090848 + -2 y = 6.819090848 + -2 Combine like terms: 6.819090848 + -2 = 4.819090848 y = 4.819090848 Simplifying y = 4.819090848Subproblem 2
y + 2 = -6.819090848 Simplifying y + 2 = -6.819090848 Reorder the terms: 2 + y = -6.819090848 Solving 2 + y = -6.819090848 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -6.819090848 + -2 Combine like terms: 2 + -2 = 0 0 + y = -6.819090848 + -2 y = -6.819090848 + -2 Combine like terms: -6.819090848 + -2 = -8.819090848 y = -8.819090848 Simplifying y = -8.819090848Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.819090848, -8.819090848}
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