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Simplifying y2 + 8y = 40 Reorder the terms: 8y + y2 = 40 Solving 8y + y2 = 40 Solving for variable 'y'. Reorder the terms: -40 + 8y + y2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 8y + 40 + y2 = 0 + 40 Reorder the terms: -40 + 40 + 8y + y2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 8y + y2 = 0 + 40 8y + y2 = 0 + 40 Combine like terms: 0 + 40 = 40 8y + y2 = 40 The y term is 8y. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8y + 16 + y2 = 40 + 16 Reorder the terms: 16 + 8y + y2 = 40 + 16 Combine like terms: 40 + 16 = 56 16 + 8y + y2 = 56 Factor a perfect square on the left side: (y + 4)(y + 4) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (y + 4) equal to 7.483314774 and -7.483314774.Subproblem 1
y + 4 = 7.483314774 Simplifying y + 4 = 7.483314774 Reorder the terms: 4 + y = 7.483314774 Solving 4 + y = 7.483314774 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 7.483314774 + -4 Combine like terms: 4 + -4 = 0 0 + y = 7.483314774 + -4 y = 7.483314774 + -4 Combine like terms: 7.483314774 + -4 = 3.483314774 y = 3.483314774 Simplifying y = 3.483314774Subproblem 2
y + 4 = -7.483314774 Simplifying y + 4 = -7.483314774 Reorder the terms: 4 + y = -7.483314774 Solving 4 + y = -7.483314774 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = -7.483314774 + -4 Combine like terms: 4 + -4 = 0 0 + y = -7.483314774 + -4 y = -7.483314774 + -4 Combine like terms: -7.483314774 + -4 = -11.483314774 y = -11.483314774 Simplifying y = -11.483314774Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.483314774, -11.483314774}
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