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Simplifying y2 + -150y + 125 = 0 Reorder the terms: 125 + -150y + y2 = 0 Solving 125 + -150y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-125' to each side of the equation. 125 + -150y + -125 + y2 = 0 + -125 Reorder the terms: 125 + -125 + -150y + y2 = 0 + -125 Combine like terms: 125 + -125 = 0 0 + -150y + y2 = 0 + -125 -150y + y2 = 0 + -125 Combine like terms: 0 + -125 = -125 -150y + y2 = -125 The y term is -150y. Take half its coefficient (-75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. -150y + 5625 + y2 = -125 + 5625 Reorder the terms: 5625 + -150y + y2 = -125 + 5625 Combine like terms: -125 + 5625 = 5500 5625 + -150y + y2 = 5500 Factor a perfect square on the left side: (y + -75)(y + -75) = 5500 Calculate the square root of the right side: 74.161984871 Break this problem into two subproblems by setting (y + -75) equal to 74.161984871 and -74.161984871.Subproblem 1
y + -75 = 74.161984871 Simplifying y + -75 = 74.161984871 Reorder the terms: -75 + y = 74.161984871 Solving -75 + y = 74.161984871 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + y = 74.161984871 + 75 Combine like terms: -75 + 75 = 0 0 + y = 74.161984871 + 75 y = 74.161984871 + 75 Combine like terms: 74.161984871 + 75 = 149.161984871 y = 149.161984871 Simplifying y = 149.161984871Subproblem 2
y + -75 = -74.161984871 Simplifying y + -75 = -74.161984871 Reorder the terms: -75 + y = -74.161984871 Solving -75 + y = -74.161984871 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + y = -74.161984871 + 75 Combine like terms: -75 + 75 = 0 0 + y = -74.161984871 + 75 y = -74.161984871 + 75 Combine like terms: -74.161984871 + 75 = 0.838015129 y = 0.838015129 Simplifying y = 0.838015129Solution
The solution to the problem is based on the solutions from the subproblems. y = {149.161984871, 0.838015129}
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