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Simplifying y2 + -1y = 28 Reorder the terms: -1y + y2 = 28 Solving -1y + y2 = 28 Solving for variable 'y'. Reorder the terms: -28 + -1y + y2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -1y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -1y + 28 + y2 = 0 + 28 Reorder the terms: -28 + 28 + -1y + y2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -1y + y2 = 0 + 28 -1y + y2 = 0 + 28 Combine like terms: 0 + 28 = 28 -1y + y2 = 28 The y term is -1y. 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 = 28 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 28 + 0.25 Combine like terms: 28 + 0.25 = 28.25 0.25 + -1y + y2 = 28.25 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (y + -0.5) equal to 5.315072906 and -5.315072906.Subproblem 1
y + -0.5 = 5.315072906 Simplifying y + -0.5 = 5.315072906 Reorder the terms: -0.5 + y = 5.315072906 Solving -0.5 + y = 5.315072906 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 = 5.315072906 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 5.315072906 + 0.5 y = 5.315072906 + 0.5 Combine like terms: 5.315072906 + 0.5 = 5.815072906 y = 5.815072906 Simplifying y = 5.815072906Subproblem 2
y + -0.5 = -5.315072906 Simplifying y + -0.5 = -5.315072906 Reorder the terms: -0.5 + y = -5.315072906 Solving -0.5 + y = -5.315072906 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 = -5.315072906 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -5.315072906 + 0.5 y = -5.315072906 + 0.5 Combine like terms: -5.315072906 + 0.5 = -4.815072906 y = -4.815072906 Simplifying y = -4.815072906Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.815072906, -4.815072906}
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