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Simplifying x2 + 11x + -55 = 0 Reorder the terms: -55 + 11x + x2 = 0 Solving -55 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 11x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + 11x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 11x + x2 = 0 + 55 11x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 11x + x2 = 55 The x term is 11x. 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. 11x + 30.25 + x2 = 55 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 55 + 30.25 Combine like terms: 55 + 30.25 = 85.25 30.25 + 11x + x2 = 85.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 85.25 Calculate the square root of the right side: 9.233092656 Break this problem into two subproblems by setting (x + 5.5) equal to 9.233092656 and -9.233092656.Subproblem 1
x + 5.5 = 9.233092656 Simplifying x + 5.5 = 9.233092656 Reorder the terms: 5.5 + x = 9.233092656 Solving 5.5 + x = 9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 9.233092656 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 9.233092656 + -5.5 x = 9.233092656 + -5.5 Combine like terms: 9.233092656 + -5.5 = 3.733092656 x = 3.733092656 Simplifying x = 3.733092656Subproblem 2
x + 5.5 = -9.233092656 Simplifying x + 5.5 = -9.233092656 Reorder the terms: 5.5 + x = -9.233092656 Solving 5.5 + x = -9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -9.233092656 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -9.233092656 + -5.5 x = -9.233092656 + -5.5 Combine like terms: -9.233092656 + -5.5 = -14.733092656 x = -14.733092656 Simplifying x = -14.733092656Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.733092656, -14.733092656}
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