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Simplifying y2 + 8y + -196 = 0 Reorder the terms: -196 + 8y + y2 = 0 Solving -196 + 8y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + 8y + 196 + y2 = 0 + 196 Reorder the terms: -196 + 196 + 8y + y2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 8y + y2 = 0 + 196 8y + y2 = 0 + 196 Combine like terms: 0 + 196 = 196 8y + y2 = 196 The y term is 8y. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8y + 16 + y2 = 196 + 16 Reorder the terms: 16 + 8y + y2 = 196 + 16 Combine like terms: 196 + 16 = 212 16 + 8y + y2 = 212 Factor a perfect square on the left side: (y + 4)(y + 4) = 212 Calculate the square root of the right side: 14.560219779 Break this problem into two subproblems by setting (y + 4) equal to 14.560219779 and -14.560219779.Subproblem 1
y + 4 = 14.560219779 Simplifying y + 4 = 14.560219779 Reorder the terms: 4 + y = 14.560219779 Solving 4 + y = 14.560219779 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 14.560219779 + -4 Combine like terms: 4 + -4 = 0 0 + y = 14.560219779 + -4 y = 14.560219779 + -4 Combine like terms: 14.560219779 + -4 = 10.560219779 y = 10.560219779 Simplifying y = 10.560219779Subproblem 2
y + 4 = -14.560219779 Simplifying y + 4 = -14.560219779 Reorder the terms: 4 + y = -14.560219779 Solving 4 + y = -14.560219779 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = -14.560219779 + -4 Combine like terms: 4 + -4 = 0 0 + y = -14.560219779 + -4 y = -14.560219779 + -4 Combine like terms: -14.560219779 + -4 = -18.560219779 y = -18.560219779 Simplifying y = -18.560219779Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.560219779, -18.560219779}
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