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Simplifying 121 = 49 + y2 + -2y + 1 Reorder the terms: 121 = 49 + 1 + -2y + y2 Combine like terms: 49 + 1 = 50 121 = 50 + -2y + y2 Solving 121 = 50 + -2y + y2 Solving for variable 'y'. Combine like terms: 121 + -50 = 71 71 + 2y + -1y2 = 50 + -2y + y2 + -50 + 2y + -1y2 Reorder the terms: 71 + 2y + -1y2 = 50 + -50 + -2y + 2y + y2 + -1y2 Combine like terms: 50 + -50 = 0 71 + 2y + -1y2 = 0 + -2y + 2y + y2 + -1y2 71 + 2y + -1y2 = -2y + 2y + y2 + -1y2 Combine like terms: -2y + 2y = 0 71 + 2y + -1y2 = 0 + y2 + -1y2 71 + 2y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 71 + 2y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -71 + -2y + y2 = 0 Move the constant term to the right: Add '71' to each side of the equation. -71 + -2y + 71 + y2 = 0 + 71 Reorder the terms: -71 + 71 + -2y + y2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + -2y + y2 = 0 + 71 -2y + y2 = 0 + 71 Combine like terms: 0 + 71 = 71 -2y + y2 = 71 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 = 71 + 1 Reorder the terms: 1 + -2y + y2 = 71 + 1 Combine like terms: 71 + 1 = 72 1 + -2y + y2 = 72 Factor a perfect square on the left side: (y + -1)(y + -1) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (y + -1) equal to 8.485281374 and -8.485281374.Subproblem 1
y + -1 = 8.485281374 Simplifying y + -1 = 8.485281374 Reorder the terms: -1 + y = 8.485281374 Solving -1 + y = 8.485281374 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 = 8.485281374 + 1 Combine like terms: -1 + 1 = 0 0 + y = 8.485281374 + 1 y = 8.485281374 + 1 Combine like terms: 8.485281374 + 1 = 9.485281374 y = 9.485281374 Simplifying y = 9.485281374Subproblem 2
y + -1 = -8.485281374 Simplifying y + -1 = -8.485281374 Reorder the terms: -1 + y = -8.485281374 Solving -1 + y = -8.485281374 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 = -8.485281374 + 1 Combine like terms: -1 + 1 = 0 0 + y = -8.485281374 + 1 y = -8.485281374 + 1 Combine like terms: -8.485281374 + 1 = -7.485281374 y = -7.485281374 Simplifying y = -7.485281374Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.485281374, -7.485281374}
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