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Simplifying y2 + -10y + -11 = 1 Reorder the terms: -11 + -10y + y2 = 1 Solving -11 + -10y + y2 = 1 Solving for variable 'y'. Reorder the terms: -11 + -1 + -10y + y2 = 1 + -1 Combine like terms: -11 + -1 = -12 -12 + -10y + y2 = 1 + -1 Combine like terms: 1 + -1 = 0 -12 + -10y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -10y + 12 + y2 = 0 + 12 Reorder the terms: -12 + 12 + -10y + y2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -10y + y2 = 0 + 12 -10y + y2 = 0 + 12 Combine like terms: 0 + 12 = 12 -10y + y2 = 12 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 = 12 + 25 Reorder the terms: 25 + -10y + y2 = 12 + 25 Combine like terms: 12 + 25 = 37 25 + -10y + y2 = 37 Factor a perfect square on the left side: (y + -5)(y + -5) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (y + -5) equal to 6.08276253 and -6.08276253.Subproblem 1
y + -5 = 6.08276253 Simplifying y + -5 = 6.08276253 Reorder the terms: -5 + y = 6.08276253 Solving -5 + y = 6.08276253 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 = 6.08276253 + 5 Combine like terms: -5 + 5 = 0 0 + y = 6.08276253 + 5 y = 6.08276253 + 5 Combine like terms: 6.08276253 + 5 = 11.08276253 y = 11.08276253 Simplifying y = 11.08276253Subproblem 2
y + -5 = -6.08276253 Simplifying y + -5 = -6.08276253 Reorder the terms: -5 + y = -6.08276253 Solving -5 + y = -6.08276253 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 = -6.08276253 + 5 Combine like terms: -5 + 5 = 0 0 + y = -6.08276253 + 5 y = -6.08276253 + 5 Combine like terms: -6.08276253 + 5 = -1.08276253 y = -1.08276253 Simplifying y = -1.08276253Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.08276253, -1.08276253}
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