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Simplifying y2 + 2y = 57 Reorder the terms: 2y + y2 = 57 Solving 2y + y2 = 57 Solving for variable 'y'. Reorder the terms: -57 + 2y + y2 = 57 + -57 Combine like terms: 57 + -57 = 0 -57 + 2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '57' to each side of the equation. -57 + 2y + 57 + y2 = 0 + 57 Reorder the terms: -57 + 57 + 2y + y2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + 2y + y2 = 0 + 57 2y + y2 = 0 + 57 Combine like terms: 0 + 57 = 57 2y + y2 = 57 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 = 57 + 1 Reorder the terms: 1 + 2y + y2 = 57 + 1 Combine like terms: 57 + 1 = 58 1 + 2y + y2 = 58 Factor a perfect square on the left side: (y + 1)(y + 1) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (y + 1) equal to 7.615773106 and -7.615773106.Subproblem 1
y + 1 = 7.615773106 Simplifying y + 1 = 7.615773106 Reorder the terms: 1 + y = 7.615773106 Solving 1 + y = 7.615773106 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 = 7.615773106 + -1 Combine like terms: 1 + -1 = 0 0 + y = 7.615773106 + -1 y = 7.615773106 + -1 Combine like terms: 7.615773106 + -1 = 6.615773106 y = 6.615773106 Simplifying y = 6.615773106Subproblem 2
y + 1 = -7.615773106 Simplifying y + 1 = -7.615773106 Reorder the terms: 1 + y = -7.615773106 Solving 1 + y = -7.615773106 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 = -7.615773106 + -1 Combine like terms: 1 + -1 = 0 0 + y = -7.615773106 + -1 y = -7.615773106 + -1 Combine like terms: -7.615773106 + -1 = -8.615773106 y = -8.615773106 Simplifying y = -8.615773106Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.615773106, -8.615773106}
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