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Simplifying 5.75y + y2 = 7.5 Solving 5.75y + y2 = 7.5 Solving for variable 'y'. Reorder the terms: -7.5 + 5.75y + y2 = 7.5 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 -7.5 + 5.75y + y2 = 0.0 Begin completing the square. Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 5.75y + 7.5 + y2 = 0.0 + 7.5 Reorder the terms: -7.5 + 7.5 + 5.75y + y2 = 0.0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 5.75y + y2 = 0.0 + 7.5 5.75y + y2 = 0.0 + 7.5 Combine like terms: 0.0 + 7.5 = 7.5 5.75y + y2 = 7.5 The y term is 5.75y. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75y + 8.265625 + y2 = 7.5 + 8.265625 Reorder the terms: 8.265625 + 5.75y + y2 = 7.5 + 8.265625 Combine like terms: 7.5 + 8.265625 = 15.765625 8.265625 + 5.75y + y2 = 15.765625 Factor a perfect square on the left side: (y + 2.875)(y + 2.875) = 15.765625 Calculate the square root of the right side: 3.970595044 Break this problem into two subproblems by setting (y + 2.875) equal to 3.970595044 and -3.970595044.Subproblem 1
y + 2.875 = 3.970595044 Simplifying y + 2.875 = 3.970595044 Reorder the terms: 2.875 + y = 3.970595044 Solving 2.875 + y = 3.970595044 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + y = 3.970595044 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + y = 3.970595044 + -2.875 y = 3.970595044 + -2.875 Combine like terms: 3.970595044 + -2.875 = 1.095595044 y = 1.095595044 Simplifying y = 1.095595044Subproblem 2
y + 2.875 = -3.970595044 Simplifying y + 2.875 = -3.970595044 Reorder the terms: 2.875 + y = -3.970595044 Solving 2.875 + y = -3.970595044 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + y = -3.970595044 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + y = -3.970595044 + -2.875 y = -3.970595044 + -2.875 Combine like terms: -3.970595044 + -2.875 = -6.845595044 y = -6.845595044 Simplifying y = -6.845595044Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.095595044, -6.845595044}
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