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Simplifying x2 + -3x + -11 = 0 Reorder the terms: -11 + -3x + x2 = 0 Solving -11 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -3x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -3x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -3x + x2 = 0 + 11 -3x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -3x + x2 = 11 The x term is -3x. 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. -3x + 2.25 + x2 = 11 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 11 + 2.25 Combine like terms: 11 + 2.25 = 13.25 2.25 + -3x + x2 = 13.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + -1.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x + -1.5 = 3.640054945 Simplifying x + -1.5 = 3.640054945 Reorder the terms: -1.5 + x = 3.640054945 Solving -1.5 + x = 3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.640054945 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.640054945 + 1.5 x = 3.640054945 + 1.5 Combine like terms: 3.640054945 + 1.5 = 5.140054945 x = 5.140054945 Simplifying x = 5.140054945Subproblem 2
x + -1.5 = -3.640054945 Simplifying x + -1.5 = -3.640054945 Reorder the terms: -1.5 + x = -3.640054945 Solving -1.5 + x = -3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.640054945 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.640054945 + 1.5 x = -3.640054945 + 1.5 Combine like terms: -3.640054945 + 1.5 = -2.140054945 x = -2.140054945 Simplifying x = -2.140054945Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.140054945, -2.140054945}
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