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Simplifying y2 + 2y + -199 = 0 Reorder the terms: -199 + 2y + y2 = 0 Solving -199 + 2y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '199' to each side of the equation. -199 + 2y + 199 + y2 = 0 + 199 Reorder the terms: -199 + 199 + 2y + y2 = 0 + 199 Combine like terms: -199 + 199 = 0 0 + 2y + y2 = 0 + 199 2y + y2 = 0 + 199 Combine like terms: 0 + 199 = 199 2y + y2 = 199 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 199 + 1 Reorder the terms: 1 + 2y + y2 = 199 + 1 Combine like terms: 199 + 1 = 200 1 + 2y + y2 = 200 Factor a perfect square on the left side: (y + 1)(y + 1) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (y + 1) equal to 14.142135624 and -14.142135624.Subproblem 1
y + 1 = 14.142135624 Simplifying y + 1 = 14.142135624 Reorder the terms: 1 + y = 14.142135624 Solving 1 + y = 14.142135624 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 14.142135624 + -1 Combine like terms: 1 + -1 = 0 0 + y = 14.142135624 + -1 y = 14.142135624 + -1 Combine like terms: 14.142135624 + -1 = 13.142135624 y = 13.142135624 Simplifying y = 13.142135624Subproblem 2
y + 1 = -14.142135624 Simplifying y + 1 = -14.142135624 Reorder the terms: 1 + y = -14.142135624 Solving 1 + y = -14.142135624 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -14.142135624 + -1 Combine like terms: 1 + -1 = 0 0 + y = -14.142135624 + -1 y = -14.142135624 + -1 Combine like terms: -14.142135624 + -1 = -15.142135624 y = -15.142135624 Simplifying y = -15.142135624Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.142135624, -15.142135624}
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