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Simplifying y2 + -10y + 22 = 0 Reorder the terms: 22 + -10y + y2 = 0 Solving 22 + -10y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + -10y + -22 + y2 = 0 + -22 Reorder the terms: 22 + -22 + -10y + y2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -10y + y2 = 0 + -22 -10y + y2 = 0 + -22 Combine like terms: 0 + -22 = -22 -10y + y2 = -22 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 = -22 + 25 Reorder the terms: 25 + -10y + y2 = -22 + 25 Combine like terms: -22 + 25 = 3 25 + -10y + y2 = 3 Factor a perfect square on the left side: (y + -5)(y + -5) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (y + -5) equal to 1.732050808 and -1.732050808.Subproblem 1
y + -5 = 1.732050808 Simplifying y + -5 = 1.732050808 Reorder the terms: -5 + y = 1.732050808 Solving -5 + y = 1.732050808 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 = 1.732050808 + 5 Combine like terms: -5 + 5 = 0 0 + y = 1.732050808 + 5 y = 1.732050808 + 5 Combine like terms: 1.732050808 + 5 = 6.732050808 y = 6.732050808 Simplifying y = 6.732050808Subproblem 2
y + -5 = -1.732050808 Simplifying y + -5 = -1.732050808 Reorder the terms: -5 + y = -1.732050808 Solving -5 + y = -1.732050808 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 = -1.732050808 + 5 Combine like terms: -5 + 5 = 0 0 + y = -1.732050808 + 5 y = -1.732050808 + 5 Combine like terms: -1.732050808 + 5 = 3.267949192 y = 3.267949192 Simplifying y = 3.267949192Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.732050808, 3.267949192}
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