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Simplifying 0 = x2 + -11x + -104 Reorder the terms: 0 = -104 + -11x + x2 Solving 0 = -104 + -11x + x2 Solving for variable 'x'. Combine like terms: 0 + 104 = 104 104 + 11x + -1x2 = -104 + -11x + x2 + 104 + 11x + -1x2 Reorder the terms: 104 + 11x + -1x2 = -104 + 104 + -11x + 11x + x2 + -1x2 Combine like terms: -104 + 104 = 0 104 + 11x + -1x2 = 0 + -11x + 11x + x2 + -1x2 104 + 11x + -1x2 = -11x + 11x + x2 + -1x2 Combine like terms: -11x + 11x = 0 104 + 11x + -1x2 = 0 + x2 + -1x2 104 + 11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 104 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -104 + -11x + x2 = 0 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 = 17.086630226 x = 17.086630226 Simplifying x = 17.086630226Subproblem 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 = -6.086630226 x = -6.086630226 Simplifying x = -6.086630226Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.086630226, -6.086630226}
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