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Simplifying y2 + -22y + 1 = 0 Reorder the terms: 1 + -22y + y2 = 0 Solving 1 + -22y + 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 + -22y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + -22y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -22y + y2 = 0 + -1 -22y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -22y + y2 = -1 The y term is -22y. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22y + 121 + y2 = -1 + 121 Reorder the terms: 121 + -22y + y2 = -1 + 121 Combine like terms: -1 + 121 = 120 121 + -22y + y2 = 120 Factor a perfect square on the left side: (y + -11)(y + -11) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (y + -11) equal to 10.95445115 and -10.95445115.Subproblem 1
y + -11 = 10.95445115 Simplifying y + -11 = 10.95445115 Reorder the terms: -11 + y = 10.95445115 Solving -11 + y = 10.95445115 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + y = 10.95445115 + 11 Combine like terms: -11 + 11 = 0 0 + y = 10.95445115 + 11 y = 10.95445115 + 11 Combine like terms: 10.95445115 + 11 = 21.95445115 y = 21.95445115 Simplifying y = 21.95445115Subproblem 2
y + -11 = -10.95445115 Simplifying y + -11 = -10.95445115 Reorder the terms: -11 + y = -10.95445115 Solving -11 + y = -10.95445115 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + y = -10.95445115 + 11 Combine like terms: -11 + 11 = 0 0 + y = -10.95445115 + 11 y = -10.95445115 + 11 Combine like terms: -10.95445115 + 11 = 0.04554885 y = 0.04554885 Simplifying y = 0.04554885Solution
The solution to the problem is based on the solutions from the subproblems. y = {21.95445115, 0.04554885}
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