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Simplifying y2 + 4y + -198 = 0 Reorder the terms: -198 + 4y + y2 = 0 Solving -198 + 4y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '198' to each side of the equation. -198 + 4y + 198 + y2 = 0 + 198 Reorder the terms: -198 + 198 + 4y + y2 = 0 + 198 Combine like terms: -198 + 198 = 0 0 + 4y + y2 = 0 + 198 4y + y2 = 0 + 198 Combine like terms: 0 + 198 = 198 4y + y2 = 198 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 198 + 4 Reorder the terms: 4 + 4y + y2 = 198 + 4 Combine like terms: 198 + 4 = 202 4 + 4y + y2 = 202 Factor a perfect square on the left side: (y + 2)(y + 2) = 202 Calculate the square root of the right side: 14.212670404 Break this problem into two subproblems by setting (y + 2) equal to 14.212670404 and -14.212670404.Subproblem 1
y + 2 = 14.212670404 Simplifying y + 2 = 14.212670404 Reorder the terms: 2 + y = 14.212670404 Solving 2 + y = 14.212670404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 14.212670404 + -2 Combine like terms: 2 + -2 = 0 0 + y = 14.212670404 + -2 y = 14.212670404 + -2 Combine like terms: 14.212670404 + -2 = 12.212670404 y = 12.212670404 Simplifying y = 12.212670404Subproblem 2
y + 2 = -14.212670404 Simplifying y + 2 = -14.212670404 Reorder the terms: 2 + y = -14.212670404 Solving 2 + y = -14.212670404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -14.212670404 + -2 Combine like terms: 2 + -2 = 0 0 + y = -14.212670404 + -2 y = -14.212670404 + -2 Combine like terms: -14.212670404 + -2 = -16.212670404 y = -16.212670404 Simplifying y = -16.212670404Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.212670404, -16.212670404}
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