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Simplifying y2 + 85y + 875 = 0 Reorder the terms: 875 + 85y + y2 = 0 Solving 875 + 85y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-875' to each side of the equation. 875 + 85y + -875 + y2 = 0 + -875 Reorder the terms: 875 + -875 + 85y + y2 = 0 + -875 Combine like terms: 875 + -875 = 0 0 + 85y + y2 = 0 + -875 85y + y2 = 0 + -875 Combine like terms: 0 + -875 = -875 85y + y2 = -875 The y term is 85y. Take half its coefficient (42.5). Square it (1806.25) and add it to both sides. Add '1806.25' to each side of the equation. 85y + 1806.25 + y2 = -875 + 1806.25 Reorder the terms: 1806.25 + 85y + y2 = -875 + 1806.25 Combine like terms: -875 + 1806.25 = 931.25 1806.25 + 85y + y2 = 931.25 Factor a perfect square on the left side: (y + 42.5)(y + 42.5) = 931.25 Calculate the square root of the right side: 30.516389039 Break this problem into two subproblems by setting (y + 42.5) equal to 30.516389039 and -30.516389039.Subproblem 1
y + 42.5 = 30.516389039 Simplifying y + 42.5 = 30.516389039 Reorder the terms: 42.5 + y = 30.516389039 Solving 42.5 + y = 30.516389039 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-42.5' to each side of the equation. 42.5 + -42.5 + y = 30.516389039 + -42.5 Combine like terms: 42.5 + -42.5 = 0.0 0.0 + y = 30.516389039 + -42.5 y = 30.516389039 + -42.5 Combine like terms: 30.516389039 + -42.5 = -11.983610961 y = -11.983610961 Simplifying y = -11.983610961Subproblem 2
y + 42.5 = -30.516389039 Simplifying y + 42.5 = -30.516389039 Reorder the terms: 42.5 + y = -30.516389039 Solving 42.5 + y = -30.516389039 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-42.5' to each side of the equation. 42.5 + -42.5 + y = -30.516389039 + -42.5 Combine like terms: 42.5 + -42.5 = 0.0 0.0 + y = -30.516389039 + -42.5 y = -30.516389039 + -42.5 Combine like terms: -30.516389039 + -42.5 = -73.016389039 y = -73.016389039 Simplifying y = -73.016389039Solution
The solution to the problem is based on the solutions from the subproblems. y = {-11.983610961, -73.016389039}
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