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Simplifying 2y + y2 = 29 + -6 Combine like terms: 29 + -6 = 23 2y + y2 = 23 Solving 2y + y2 = 23 Solving for variable 'y'. Reorder the terms: -23 + 2y + y2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + 2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 2y + 23 + y2 = 0 + 23 Reorder the terms: -23 + 23 + 2y + y2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 2y + y2 = 0 + 23 2y + y2 = 0 + 23 Combine like terms: 0 + 23 = 23 2y + y2 = 23 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 = 23 + 1 Reorder the terms: 1 + 2y + y2 = 23 + 1 Combine like terms: 23 + 1 = 24 1 + 2y + y2 = 24 Factor a perfect square on the left side: (y + 1)(y + 1) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (y + 1) equal to 4.898979486 and -4.898979486.Subproblem 1
y + 1 = 4.898979486 Simplifying y + 1 = 4.898979486 Reorder the terms: 1 + y = 4.898979486 Solving 1 + y = 4.898979486 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 = 4.898979486 + -1 Combine like terms: 1 + -1 = 0 0 + y = 4.898979486 + -1 y = 4.898979486 + -1 Combine like terms: 4.898979486 + -1 = 3.898979486 y = 3.898979486 Simplifying y = 3.898979486Subproblem 2
y + 1 = -4.898979486 Simplifying y + 1 = -4.898979486 Reorder the terms: 1 + y = -4.898979486 Solving 1 + y = -4.898979486 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 = -4.898979486 + -1 Combine like terms: 1 + -1 = 0 0 + y = -4.898979486 + -1 y = -4.898979486 + -1 Combine like terms: -4.898979486 + -1 = -5.898979486 y = -5.898979486 Simplifying y = -5.898979486Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.898979486, -5.898979486}
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