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Simplifying 121 = 49 + y2 + -1y + 1 Reorder the terms: 121 = 49 + 1 + -1y + y2 Combine like terms: 49 + 1 = 50 121 = 50 + -1y + y2 Solving 121 = 50 + -1y + y2 Solving for variable 'y'. Combine like terms: 121 + -50 = 71 71 + y + -1y2 = 50 + -1y + y2 + -50 + y + -1y2 Reorder the terms: 71 + y + -1y2 = 50 + -50 + -1y + y + y2 + -1y2 Combine like terms: 50 + -50 = 0 71 + y + -1y2 = 0 + -1y + y + y2 + -1y2 71 + y + -1y2 = -1y + y + y2 + -1y2 Combine like terms: -1y + y = 0 71 + y + -1y2 = 0 + y2 + -1y2 71 + y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 71 + y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -71 + -1y + y2 = 0 Move the constant term to the right: Add '71' to each side of the equation. -71 + -1y + 71 + y2 = 0 + 71 Reorder the terms: -71 + 71 + -1y + y2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + -1y + y2 = 0 + 71 -1y + y2 = 0 + 71 Combine like terms: 0 + 71 = 71 -1y + y2 = 71 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 71 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 71 + 0.25 Combine like terms: 71 + 0.25 = 71.25 0.25 + -1y + y2 = 71.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 71.25 Calculate the square root of the right side: 8.440971508 Break this problem into two subproblems by setting (y + 0.5) equal to 8.440971508 and -8.440971508.Subproblem 1
y + 0.5 = 8.440971508 Simplifying y + 0.5 = 8.440971508 Reorder the terms: 0.5 + y = 8.440971508 Solving 0.5 + y = 8.440971508 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 8.440971508 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 8.440971508 + -0.5 y = 8.440971508 + -0.5 Combine like terms: 8.440971508 + -0.5 = 7.940971508 y = 7.940971508 Simplifying y = 7.940971508Subproblem 2
y + 0.5 = -8.440971508 Simplifying y + 0.5 = -8.440971508 Reorder the terms: 0.5 + y = -8.440971508 Solving 0.5 + y = -8.440971508 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -8.440971508 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -8.440971508 + -0.5 y = -8.440971508 + -0.5 Combine like terms: -8.440971508 + -0.5 = -8.940971508 y = -8.940971508 Simplifying y = -8.940971508Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.940971508, -8.940971508}
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