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Simplifying y2 + -6y + -334 = 0 Reorder the terms: -334 + -6y + y2 = 0 Solving -334 + -6y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '334' to each side of the equation. -334 + -6y + 334 + y2 = 0 + 334 Reorder the terms: -334 + 334 + -6y + y2 = 0 + 334 Combine like terms: -334 + 334 = 0 0 + -6y + y2 = 0 + 334 -6y + y2 = 0 + 334 Combine like terms: 0 + 334 = 334 -6y + y2 = 334 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 = 334 + 9 Reorder the terms: 9 + -6y + y2 = 334 + 9 Combine like terms: 334 + 9 = 343 9 + -6y + y2 = 343 Factor a perfect square on the left side: (y + -3)(y + -3) = 343 Calculate the square root of the right side: 18.520259177 Break this problem into two subproblems by setting (y + -3) equal to 18.520259177 and -18.520259177.Subproblem 1
y + -3 = 18.520259177 Simplifying y + -3 = 18.520259177 Reorder the terms: -3 + y = 18.520259177 Solving -3 + y = 18.520259177 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 = 18.520259177 + 3 Combine like terms: -3 + 3 = 0 0 + y = 18.520259177 + 3 y = 18.520259177 + 3 Combine like terms: 18.520259177 + 3 = 21.520259177 y = 21.520259177 Simplifying y = 21.520259177Subproblem 2
y + -3 = -18.520259177 Simplifying y + -3 = -18.520259177 Reorder the terms: -3 + y = -18.520259177 Solving -3 + y = -18.520259177 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 = -18.520259177 + 3 Combine like terms: -3 + 3 = 0 0 + y = -18.520259177 + 3 y = -18.520259177 + 3 Combine like terms: -18.520259177 + 3 = -15.520259177 y = -15.520259177 Simplifying y = -15.520259177Solution
The solution to the problem is based on the solutions from the subproblems. y = {21.520259177, -15.520259177}
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