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Simplifying y2 + 10y + -1 = 0 Reorder the terms: -1 + 10y + y2 = 0 Solving -1 + 10y + 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 + 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 = 0.099019514 y = 0.099019514 Simplifying y = 0.099019514Subproblem 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 = -10.099019514 y = -10.099019514 Simplifying y = -10.099019514Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.099019514, -10.099019514}
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