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Simplifying 3 = y2 + -2y + -2 Reorder the terms: 3 = -2 + -2y + y2 Solving 3 = -2 + -2y + y2 Solving for variable 'y'. Combine like terms: 3 + 2 = 5 5 + 2y + -1y2 = -2 + -2y + y2 + 2 + 2y + -1y2 Reorder the terms: 5 + 2y + -1y2 = -2 + 2 + -2y + 2y + y2 + -1y2 Combine like terms: -2 + 2 = 0 5 + 2y + -1y2 = 0 + -2y + 2y + y2 + -1y2 5 + 2y + -1y2 = -2y + 2y + y2 + -1y2 Combine like terms: -2y + 2y = 0 5 + 2y + -1y2 = 0 + y2 + -1y2 5 + 2y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 5 + 2y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -2y + y2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -2y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + -2y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2y + y2 = 0 + 5 -2y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2y + y2 = 5 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 5 + 1 Reorder the terms: 1 + -2y + y2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + -2y + y2 = 6 Factor a perfect square on the left side: (y + -1)(y + -1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (y + -1) equal to 2.449489743 and -2.449489743.Subproblem 1
y + -1 = 2.449489743 Simplifying y + -1 = 2.449489743 Reorder the terms: -1 + y = 2.449489743 Solving -1 + y = 2.449489743 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + y = 2.449489743 + 1 y = 2.449489743 + 1 Combine like terms: 2.449489743 + 1 = 3.449489743 y = 3.449489743 Simplifying y = 3.449489743Subproblem 2
y + -1 = -2.449489743 Simplifying y + -1 = -2.449489743 Reorder the terms: -1 + y = -2.449489743 Solving -1 + y = -2.449489743 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + y = -2.449489743 + 1 y = -2.449489743 + 1 Combine like terms: -2.449489743 + 1 = -1.449489743 y = -1.449489743 Simplifying y = -1.449489743Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.449489743, -1.449489743}
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