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Simplifying y2 + -10y = 1 Reorder the terms: -10y + y2 = 1 Solving -10y + y2 = 1 Solving for variable 'y'. Reorder the terms: -1 + -10y + y2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -10y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -10y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -10y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -10y + y2 = 0 + 1 -10y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -10y + y2 = 1 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = 1 + 25 Reorder the terms: 25 + -10y + y2 = 1 + 25 Combine like terms: 1 + 25 = 26 25 + -10y + y2 = 26 Factor a perfect square on the left side: (y + -5)(y + -5) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (y + -5) equal to 5.099019514 and -5.099019514.Subproblem 1
y + -5 = 5.099019514 Simplifying y + -5 = 5.099019514 Reorder the terms: -5 + y = 5.099019514 Solving -5 + y = 5.099019514 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 5.099019514 + 5 Combine like terms: -5 + 5 = 0 0 + y = 5.099019514 + 5 y = 5.099019514 + 5 Combine like terms: 5.099019514 + 5 = 10.099019514 y = 10.099019514 Simplifying y = 10.099019514Subproblem 2
y + -5 = -5.099019514 Simplifying y + -5 = -5.099019514 Reorder the terms: -5 + y = -5.099019514 Solving -5 + y = -5.099019514 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -5.099019514 + 5 Combine like terms: -5 + 5 = 0 0 + y = -5.099019514 + 5 y = -5.099019514 + 5 Combine like terms: -5.099019514 + 5 = -0.099019514 y = -0.099019514 Simplifying y = -0.099019514Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.099019514, -0.099019514}
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