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Simplifying y2 + -20y + 71 = 0 Reorder the terms: 71 + -20y + y2 = 0 Solving 71 + -20y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-71' to each side of the equation. 71 + -20y + -71 + y2 = 0 + -71 Reorder the terms: 71 + -71 + -20y + y2 = 0 + -71 Combine like terms: 71 + -71 = 0 0 + -20y + y2 = 0 + -71 -20y + y2 = 0 + -71 Combine like terms: 0 + -71 = -71 -20y + y2 = -71 The y term is -20y. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20y + 100 + y2 = -71 + 100 Reorder the terms: 100 + -20y + y2 = -71 + 100 Combine like terms: -71 + 100 = 29 100 + -20y + y2 = 29 Factor a perfect square on the left side: (y + -10)(y + -10) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (y + -10) equal to 5.385164807 and -5.385164807.Subproblem 1
y + -10 = 5.385164807 Simplifying y + -10 = 5.385164807 Reorder the terms: -10 + y = 5.385164807 Solving -10 + y = 5.385164807 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = 5.385164807 + 10 Combine like terms: -10 + 10 = 0 0 + y = 5.385164807 + 10 y = 5.385164807 + 10 Combine like terms: 5.385164807 + 10 = 15.385164807 y = 15.385164807 Simplifying y = 15.385164807Subproblem 2
y + -10 = -5.385164807 Simplifying y + -10 = -5.385164807 Reorder the terms: -10 + y = -5.385164807 Solving -10 + y = -5.385164807 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = -5.385164807 + 10 Combine like terms: -10 + 10 = 0 0 + y = -5.385164807 + 10 y = -5.385164807 + 10 Combine like terms: -5.385164807 + 10 = 4.614835193 y = 4.614835193 Simplifying y = 4.614835193Solution
The solution to the problem is based on the solutions from the subproblems. y = {15.385164807, 4.614835193}
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