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Simplifying y2 + -3y + -11 = 0 Reorder the terms: -11 + -3y + y2 = 0 Solving -11 + -3y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -3y + 11 + y2 = 0 + 11 Reorder the terms: -11 + 11 + -3y + y2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -3y + y2 = 0 + 11 -3y + y2 = 0 + 11 Combine like terms: 0 + 11 = 11 -3y + y2 = 11 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 11 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 11 + 2.25 Combine like terms: 11 + 2.25 = 13.25 2.25 + -3y + y2 = 13.25 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (y + -1.5) equal to 3.640054945 and -3.640054945.Subproblem 1
y + -1.5 = 3.640054945 Simplifying y + -1.5 = 3.640054945 Reorder the terms: -1.5 + y = 3.640054945 Solving -1.5 + y = 3.640054945 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 3.640054945 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 3.640054945 + 1.5 y = 3.640054945 + 1.5 Combine like terms: 3.640054945 + 1.5 = 5.140054945 y = 5.140054945 Simplifying y = 5.140054945Subproblem 2
y + -1.5 = -3.640054945 Simplifying y + -1.5 = -3.640054945 Reorder the terms: -1.5 + y = -3.640054945 Solving -1.5 + y = -3.640054945 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -3.640054945 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -3.640054945 + 1.5 y = -3.640054945 + 1.5 Combine like terms: -3.640054945 + 1.5 = -2.140054945 y = -2.140054945 Simplifying y = -2.140054945Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.140054945, -2.140054945}
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