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Simplifying (x)(x) + 11x + -104 = 0 Multiply x * x x2 + 11x + -104 = 0 Reorder the terms: -104 + 11x + x2 = 0 Solving -104 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + 11x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + 11x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + 11x + x2 = 0 + 104 11x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 11x + x2 = 104 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 = 104 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 104 + 30.25 Combine like terms: 104 + 30.25 = 134.25 30.25 + 11x + x2 = 134.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 134.25 Calculate the square root of the right side: 11.586630226 Break this problem into two subproblems by setting (x + 5.5) equal to 11.586630226 and -11.586630226.Subproblem 1
x + 5.5 = 11.586630226 Simplifying x + 5.5 = 11.586630226 Reorder the terms: 5.5 + x = 11.586630226 Solving 5.5 + x = 11.586630226 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 = 11.586630226 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 11.586630226 + -5.5 x = 11.586630226 + -5.5 Combine like terms: 11.586630226 + -5.5 = 6.086630226 x = 6.086630226 Simplifying x = 6.086630226Subproblem 2
x + 5.5 = -11.586630226 Simplifying x + 5.5 = -11.586630226 Reorder the terms: 5.5 + x = -11.586630226 Solving 5.5 + x = -11.586630226 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 = -11.586630226 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -11.586630226 + -5.5 x = -11.586630226 + -5.5 Combine like terms: -11.586630226 + -5.5 = -17.086630226 x = -17.086630226 Simplifying x = -17.086630226Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.086630226, -17.086630226}
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