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Simplifying y2 + -2.309y + 1 = 0 Reorder the terms: 1 + -2.309y + y2 = 0 Solving 1 + -2.309y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.309y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + -2.309y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.309y + y2 = 0 + -1 -2.309y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.309y + y2 = -1 The y term is -2.309y. Take half its coefficient (-1.1545). Square it (1.33287025) and add it to both sides. Add '1.33287025' to each side of the equation. -2.309y + 1.33287025 + y2 = -1 + 1.33287025 Reorder the terms: 1.33287025 + -2.309y + y2 = -1 + 1.33287025 Combine like terms: -1 + 1.33287025 = 0.33287025 1.33287025 + -2.309y + y2 = 0.33287025 Factor a perfect square on the left side: (y + -1.1545)(y + -1.1545) = 0.33287025 Calculate the square root of the right side: 0.576949088 Break this problem into two subproblems by setting (y + -1.1545) equal to 0.576949088 and -0.576949088.Subproblem 1
y + -1.1545 = 0.576949088 Simplifying y + -1.1545 = 0.576949088 Reorder the terms: -1.1545 + y = 0.576949088 Solving -1.1545 + y = 0.576949088 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.1545' to each side of the equation. -1.1545 + 1.1545 + y = 0.576949088 + 1.1545 Combine like terms: -1.1545 + 1.1545 = 0.0000 0.0000 + y = 0.576949088 + 1.1545 y = 0.576949088 + 1.1545 Combine like terms: 0.576949088 + 1.1545 = 1.731449088 y = 1.731449088 Simplifying y = 1.731449088Subproblem 2
y + -1.1545 = -0.576949088 Simplifying y + -1.1545 = -0.576949088 Reorder the terms: -1.1545 + y = -0.576949088 Solving -1.1545 + y = -0.576949088 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.1545' to each side of the equation. -1.1545 + 1.1545 + y = -0.576949088 + 1.1545 Combine like terms: -1.1545 + 1.1545 = 0.0000 0.0000 + y = -0.576949088 + 1.1545 y = -0.576949088 + 1.1545 Combine like terms: -0.576949088 + 1.1545 = 0.577550912 y = 0.577550912 Simplifying y = 0.577550912Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.731449088, 0.577550912}
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