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Simplifying y2 + 2y + -53 = 0 Reorder the terms: -53 + 2y + y2 = 0 Solving -53 + 2y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + 2y + 53 + y2 = 0 + 53 Reorder the terms: -53 + 53 + 2y + y2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 2y + y2 = 0 + 53 2y + y2 = 0 + 53 Combine like terms: 0 + 53 = 53 2y + y2 = 53 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 = 53 + 1 Reorder the terms: 1 + 2y + y2 = 53 + 1 Combine like terms: 53 + 1 = 54 1 + 2y + y2 = 54 Factor a perfect square on the left side: (y + 1)(y + 1) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (y + 1) equal to 7.348469228 and -7.348469228.Subproblem 1
y + 1 = 7.348469228 Simplifying y + 1 = 7.348469228 Reorder the terms: 1 + y = 7.348469228 Solving 1 + y = 7.348469228 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 = 7.348469228 + -1 Combine like terms: 1 + -1 = 0 0 + y = 7.348469228 + -1 y = 7.348469228 + -1 Combine like terms: 7.348469228 + -1 = 6.348469228 y = 6.348469228 Simplifying y = 6.348469228Subproblem 2
y + 1 = -7.348469228 Simplifying y + 1 = -7.348469228 Reorder the terms: 1 + y = -7.348469228 Solving 1 + y = -7.348469228 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 = -7.348469228 + -1 Combine like terms: 1 + -1 = 0 0 + y = -7.348469228 + -1 y = -7.348469228 + -1 Combine like terms: -7.348469228 + -1 = -8.348469228 y = -8.348469228 Simplifying y = -8.348469228Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.348469228, -8.348469228}
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