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Simplifying y2 + 22y + -4 = 0 Reorder the terms: -4 + 22y + y2 = 0 Solving -4 + 22y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 22y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + 22y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 22y + y2 = 0 + 4 22y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 22y + y2 = 4 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 = 4 + 121 Reorder the terms: 121 + 22y + y2 = 4 + 121 Combine like terms: 4 + 121 = 125 121 + 22y + y2 = 125 Factor a perfect square on the left side: (y + 11)(y + 11) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (y + 11) equal to 11.180339887 and -11.180339887.Subproblem 1
y + 11 = 11.180339887 Simplifying y + 11 = 11.180339887 Reorder the terms: 11 + y = 11.180339887 Solving 11 + y = 11.180339887 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 = 11.180339887 + -11 Combine like terms: 11 + -11 = 0 0 + y = 11.180339887 + -11 y = 11.180339887 + -11 Combine like terms: 11.180339887 + -11 = 0.180339887 y = 0.180339887 Simplifying y = 0.180339887Subproblem 2
y + 11 = -11.180339887 Simplifying y + 11 = -11.180339887 Reorder the terms: 11 + y = -11.180339887 Solving 11 + y = -11.180339887 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 = -11.180339887 + -11 Combine like terms: 11 + -11 = 0 0 + y = -11.180339887 + -11 y = -11.180339887 + -11 Combine like terms: -11.180339887 + -11 = -22.180339887 y = -22.180339887 Simplifying y = -22.180339887Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.180339887, -22.180339887}
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