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Simplifying y2 + 6 = 6y Reorder the terms: 6 + y2 = 6y Solving 6 + y2 = 6y Solving for variable 'y'. Reorder the terms: 6 + -6y + y2 = 6y + -6y Combine like terms: 6y + -6y = 0 6 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -6y + -6 + y2 = 0 + -6 Reorder the terms: 6 + -6 + -6y + y2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -6y + y2 = 0 + -6 -6y + y2 = 0 + -6 Combine like terms: 0 + -6 = -6 -6y + y2 = -6 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 = -6 + 9 Reorder the terms: 9 + -6y + y2 = -6 + 9 Combine like terms: -6 + 9 = 3 9 + -6y + y2 = 3 Factor a perfect square on the left side: (y + -3)(y + -3) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (y + -3) equal to 1.732050808 and -1.732050808.Subproblem 1
y + -3 = 1.732050808 Simplifying y + -3 = 1.732050808 Reorder the terms: -3 + y = 1.732050808 Solving -3 + y = 1.732050808 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 = 1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + y = 1.732050808 + 3 y = 1.732050808 + 3 Combine like terms: 1.732050808 + 3 = 4.732050808 y = 4.732050808 Simplifying y = 4.732050808Subproblem 2
y + -3 = -1.732050808 Simplifying y + -3 = -1.732050808 Reorder the terms: -3 + y = -1.732050808 Solving -3 + y = -1.732050808 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 = -1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + y = -1.732050808 + 3 y = -1.732050808 + 3 Combine like terms: -1.732050808 + 3 = 1.267949192 y = 1.267949192 Simplifying y = 1.267949192Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.732050808, 1.267949192}
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