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Simplifying y2 = 16 + -7y Solving y2 = 16 + -7y Solving for variable 'y'. Reorder the terms: -16 + 7y + y2 = 16 + -7y + -16 + 7y Reorder the terms: -16 + 7y + y2 = 16 + -16 + -7y + 7y Combine like terms: 16 + -16 = 0 -16 + 7y + y2 = 0 + -7y + 7y -16 + 7y + y2 = -7y + 7y Combine like terms: -7y + 7y = 0 -16 + 7y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 7y + 16 + y2 = 0 + 16 Reorder the terms: -16 + 16 + 7y + y2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 7y + y2 = 0 + 16 7y + y2 = 0 + 16 Combine like terms: 0 + 16 = 16 7y + y2 = 16 The y term is 7y. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7y + 12.25 + y2 = 16 + 12.25 Reorder the terms: 12.25 + 7y + y2 = 16 + 12.25 Combine like terms: 16 + 12.25 = 28.25 12.25 + 7y + y2 = 28.25 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (y + 3.5) equal to 5.315072906 and -5.315072906.Subproblem 1
y + 3.5 = 5.315072906 Simplifying y + 3.5 = 5.315072906 Reorder the terms: 3.5 + y = 5.315072906 Solving 3.5 + y = 5.315072906 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = 5.315072906 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 5.315072906 + -3.5 y = 5.315072906 + -3.5 Combine like terms: 5.315072906 + -3.5 = 1.815072906 y = 1.815072906 Simplifying y = 1.815072906Subproblem 2
y + 3.5 = -5.315072906 Simplifying y + 3.5 = -5.315072906 Reorder the terms: 3.5 + y = -5.315072906 Solving 3.5 + y = -5.315072906 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = -5.315072906 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -5.315072906 + -3.5 y = -5.315072906 + -3.5 Combine like terms: -5.315072906 + -3.5 = -8.815072906 y = -8.815072906 Simplifying y = -8.815072906Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.815072906, -8.815072906}
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