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Simplifying y2 + 6y + -196 = 0 Reorder the terms: -196 + 6y + y2 = 0 Solving -196 + 6y + 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 + 6y + 196 + y2 = 0 + 196 Reorder the terms: -196 + 196 + 6y + y2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 6y + y2 = 0 + 196 6y + y2 = 0 + 196 Combine like terms: 0 + 196 = 196 6y + y2 = 196 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = 196 + 9 Reorder the terms: 9 + 6y + y2 = 196 + 9 Combine like terms: 196 + 9 = 205 9 + 6y + y2 = 205 Factor a perfect square on the left side: (y + 3)(y + 3) = 205 Calculate the square root of the right side: 14.317821063 Break this problem into two subproblems by setting (y + 3) equal to 14.317821063 and -14.317821063.Subproblem 1
y + 3 = 14.317821063 Simplifying y + 3 = 14.317821063 Reorder the terms: 3 + y = 14.317821063 Solving 3 + y = 14.317821063 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 14.317821063 + -3 Combine like terms: 3 + -3 = 0 0 + y = 14.317821063 + -3 y = 14.317821063 + -3 Combine like terms: 14.317821063 + -3 = 11.317821063 y = 11.317821063 Simplifying y = 11.317821063Subproblem 2
y + 3 = -14.317821063 Simplifying y + 3 = -14.317821063 Reorder the terms: 3 + y = -14.317821063 Solving 3 + y = -14.317821063 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -14.317821063 + -3 Combine like terms: 3 + -3 = 0 0 + y = -14.317821063 + -3 y = -14.317821063 + -3 Combine like terms: -14.317821063 + -3 = -17.317821063 y = -17.317821063 Simplifying y = -17.317821063Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.317821063, -17.317821063}
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