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Simplifying y2 + 2y = 5.75 Reorder the terms: 2y + y2 = 5.75 Solving 2y + y2 = 5.75 Solving for variable 'y'. Reorder the terms: -5.75 + 2y + y2 = 5.75 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 -5.75 + 2y + y2 = 0.00 Begin completing the square. Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + 2y + 5.75 + y2 = 0.00 + 5.75 Reorder the terms: -5.75 + 5.75 + 2y + y2 = 0.00 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + 2y + y2 = 0.00 + 5.75 2y + y2 = 0.00 + 5.75 Combine like terms: 0.00 + 5.75 = 5.75 2y + y2 = 5.75 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 5.75 + 1 Reorder the terms: 1 + 2y + y2 = 5.75 + 1 Combine like terms: 5.75 + 1 = 6.75 1 + 2y + y2 = 6.75 Factor a perfect square on the left side: (y + 1)(y + 1) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (y + 1) equal to 2.598076211 and -2.598076211.Subproblem 1
y + 1 = 2.598076211 Simplifying y + 1 = 2.598076211 Reorder the terms: 1 + y = 2.598076211 Solving 1 + y = 2.598076211 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 2.598076211 + -1 Combine like terms: 1 + -1 = 0 0 + y = 2.598076211 + -1 y = 2.598076211 + -1 Combine like terms: 2.598076211 + -1 = 1.598076211 y = 1.598076211 Simplifying y = 1.598076211Subproblem 2
y + 1 = -2.598076211 Simplifying y + 1 = -2.598076211 Reorder the terms: 1 + y = -2.598076211 Solving 1 + y = -2.598076211 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -2.598076211 + -1 Combine like terms: 1 + -1 = 0 0 + y = -2.598076211 + -1 y = -2.598076211 + -1 Combine like terms: -2.598076211 + -1 = -3.598076211 y = -3.598076211 Simplifying y = -3.598076211Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.598076211, -3.598076211}
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