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Simplifying y2 = 6y + 3 Reorder the terms: y2 = 3 + 6y Solving y2 = 3 + 6y Solving for variable 'y'. Reorder the terms: -3 + -6y + y2 = 3 + 6y + -3 + -6y Reorder the terms: -3 + -6y + y2 = 3 + -3 + 6y + -6y Combine like terms: 3 + -3 = 0 -3 + -6y + y2 = 0 + 6y + -6y -3 + -6y + y2 = 6y + -6y Combine like terms: 6y + -6y = 0 -3 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -6y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + -6y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6y + y2 = 0 + 3 -6y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6y + y2 = 3 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 = 3 + 9 Reorder the terms: 9 + -6y + y2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + -6y + y2 = 12 Factor a perfect square on the left side: (y + -3)(y + -3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (y + -3) equal to 3.464101615 and -3.464101615.Subproblem 1
y + -3 = 3.464101615 Simplifying y + -3 = 3.464101615 Reorder the terms: -3 + y = 3.464101615 Solving -3 + y = 3.464101615 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 = 3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + y = 3.464101615 + 3 y = 3.464101615 + 3 Combine like terms: 3.464101615 + 3 = 6.464101615 y = 6.464101615 Simplifying y = 6.464101615Subproblem 2
y + -3 = -3.464101615 Simplifying y + -3 = -3.464101615 Reorder the terms: -3 + y = -3.464101615 Solving -3 + y = -3.464101615 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 = -3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + y = -3.464101615 + 3 y = -3.464101615 + 3 Combine like terms: -3.464101615 + 3 = -0.464101615 y = -0.464101615 Simplifying y = -0.464101615Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.464101615, -0.464101615}
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