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Simplifying (-3 + y)(-3 + y) = 6 Multiply (-3 + y) * (-3 + y) (-3(-3 + y) + y(-3 + y)) = 6 ((-3 * -3 + y * -3) + y(-3 + y)) = 6 ((9 + -3y) + y(-3 + y)) = 6 (9 + -3y + (-3 * y + y * y)) = 6 (9 + -3y + (-3y + y2)) = 6 Combine like terms: -3y + -3y = -6y (9 + -6y + y2) = 6 Solving 9 + -6y + y2 = 6 Solving for variable 'y'. Reorder the terms: 9 + -6 + -6y + y2 = 6 + -6 Combine like terms: 9 + -6 = 3 3 + -6y + y2 = 6 + -6 Combine like terms: 6 + -6 = 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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