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Simplifying 0 = -1y2 + 6y + -3 Reorder the terms: 0 = -3 + 6y + -1y2 Solving 0 = -3 + 6y + -1y2 Solving for variable 'y'. Combine like terms: 0 + 3 = 3 3 + -6y + y2 = -3 + 6y + -1y2 + 3 + -6y + y2 Reorder the terms: 3 + -6y + y2 = -3 + 3 + 6y + -6y + -1y2 + y2 Combine like terms: -3 + 3 = 0 3 + -6y + y2 = 0 + 6y + -6y + -1y2 + y2 3 + -6y + y2 = 6y + -6y + -1y2 + y2 Combine like terms: 6y + -6y = 0 3 + -6y + y2 = 0 + -1y2 + y2 3 + -6y + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 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 = 6 9 + -6y + y2 = 6 Factor a perfect square on the left side: (y + -3)(y + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (y + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
y + -3 = 2.449489743 Simplifying y + -3 = 2.449489743 Reorder the terms: -3 + y = 2.449489743 Solving -3 + y = 2.449489743 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 = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + y = 2.449489743 + 3 y = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 y = 5.449489743 Simplifying y = 5.449489743Subproblem 2
y + -3 = -2.449489743 Simplifying y + -3 = -2.449489743 Reorder the terms: -3 + y = -2.449489743 Solving -3 + y = -2.449489743 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 = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + y = -2.449489743 + 3 y = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 y = 0.550510257 Simplifying y = 0.550510257Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.449489743, 0.550510257}
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