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Simplifying 108 = y(y) + 4y Multiply y * y 108 = y2 + 4y Reorder the terms: 108 = 4y + y2 Solving 108 = 4y + y2 Solving for variable 'y'. Reorder the terms: 108 + -4y + -1y2 = 4y + -4y + y2 + -1y2 Combine like terms: 4y + -4y = 0 108 + -4y + -1y2 = 0 + y2 + -1y2 108 + -4y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 108 + -4y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -108 + 4y + y2 = 0 Move the constant term to the right: Add '108' to each side of the equation. -108 + 4y + 108 + y2 = 0 + 108 Reorder the terms: -108 + 108 + 4y + y2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 4y + y2 = 0 + 108 4y + y2 = 0 + 108 Combine like terms: 0 + 108 = 108 4y + y2 = 108 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 = 108 + 4 Reorder the terms: 4 + 4y + y2 = 108 + 4 Combine like terms: 108 + 4 = 112 4 + 4y + y2 = 112 Factor a perfect square on the left side: (y + 2)(y + 2) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (y + 2) equal to 10.583005244 and -10.583005244.Subproblem 1
y + 2 = 10.583005244 Simplifying y + 2 = 10.583005244 Reorder the terms: 2 + y = 10.583005244 Solving 2 + y = 10.583005244 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 = 10.583005244 + -2 Combine like terms: 2 + -2 = 0 0 + y = 10.583005244 + -2 y = 10.583005244 + -2 Combine like terms: 10.583005244 + -2 = 8.583005244 y = 8.583005244 Simplifying y = 8.583005244Subproblem 2
y + 2 = -10.583005244 Simplifying y + 2 = -10.583005244 Reorder the terms: 2 + y = -10.583005244 Solving 2 + y = -10.583005244 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 = -10.583005244 + -2 Combine like terms: 2 + -2 = 0 0 + y = -10.583005244 + -2 y = -10.583005244 + -2 Combine like terms: -10.583005244 + -2 = -12.583005244 y = -12.583005244 Simplifying y = -12.583005244Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.583005244, -12.583005244}
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