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Simplifying y2 = 6y + -7 Reorder the terms: y2 = -7 + 6y Solving y2 = -7 + 6y Solving for variable 'y'. Reorder the terms: 7 + -6y + y2 = -7 + 6y + 7 + -6y Reorder the terms: 7 + -6y + y2 = -7 + 7 + 6y + -6y Combine like terms: -7 + 7 = 0 7 + -6y + y2 = 0 + 6y + -6y 7 + -6y + y2 = 6y + -6y Combine like terms: 6y + -6y = 0 7 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -6y + -7 + y2 = 0 + -7 Reorder the terms: 7 + -7 + -6y + y2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6y + y2 = 0 + -7 -6y + y2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6y + y2 = -7 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 = -7 + 9 Reorder the terms: 9 + -6y + y2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + -6y + y2 = 2 Factor a perfect square on the left side: (y + -3)(y + -3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (y + -3) equal to 1.414213562 and -1.414213562.Subproblem 1
y + -3 = 1.414213562 Simplifying y + -3 = 1.414213562 Reorder the terms: -3 + y = 1.414213562 Solving -3 + y = 1.414213562 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 = 1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + y = 1.414213562 + 3 y = 1.414213562 + 3 Combine like terms: 1.414213562 + 3 = 4.414213562 y = 4.414213562 Simplifying y = 4.414213562Subproblem 2
y + -3 = -1.414213562 Simplifying y + -3 = -1.414213562 Reorder the terms: -3 + y = -1.414213562 Solving -3 + y = -1.414213562 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 = -1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + y = -1.414213562 + 3 y = -1.414213562 + 3 Combine like terms: -1.414213562 + 3 = 1.585786438 y = 1.585786438 Simplifying y = 1.585786438Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.414213562, 1.585786438}
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