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Simplifying 1y2 + -28 + -11y = 0 Reorder the terms: -28 + -11y + 1y2 = 0 Solving -28 + -11y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -11y + 28 + y2 = 0 + 28 Reorder the terms: -28 + 28 + -11y + y2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -11y + y2 = 0 + 28 -11y + y2 = 0 + 28 Combine like terms: 0 + 28 = 28 -11y + y2 = 28 The y term is -11y. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11y + 30.25 + y2 = 28 + 30.25 Reorder the terms: 30.25 + -11y + y2 = 28 + 30.25 Combine like terms: 28 + 30.25 = 58.25 30.25 + -11y + y2 = 58.25 Factor a perfect square on the left side: (y + -5.5)(y + -5.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (y + -5.5) equal to 7.632168761 and -7.632168761.Subproblem 1
y + -5.5 = 7.632168761 Simplifying y + -5.5 = 7.632168761 Reorder the terms: -5.5 + y = 7.632168761 Solving -5.5 + y = 7.632168761 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = 7.632168761 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 7.632168761 + 5.5 y = 7.632168761 + 5.5 Combine like terms: 7.632168761 + 5.5 = 13.132168761 y = 13.132168761 Simplifying y = 13.132168761Subproblem 2
y + -5.5 = -7.632168761 Simplifying y + -5.5 = -7.632168761 Reorder the terms: -5.5 + y = -7.632168761 Solving -5.5 + y = -7.632168761 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = -7.632168761 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -7.632168761 + 5.5 y = -7.632168761 + 5.5 Combine like terms: -7.632168761 + 5.5 = -2.132168761 y = -2.132168761 Simplifying y = -2.132168761Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.132168761, -2.132168761}
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