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Simplifying x2 + 11x + -119 = 0 Reorder the terms: -119 + 11x + x2 = 0 Solving -119 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '119' to each side of the equation. -119 + 11x + 119 + x2 = 0 + 119 Reorder the terms: -119 + 119 + 11x + x2 = 0 + 119 Combine like terms: -119 + 119 = 0 0 + 11x + x2 = 0 + 119 11x + x2 = 0 + 119 Combine like terms: 0 + 119 = 119 11x + x2 = 119 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 = 119 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 119 + 30.25 Combine like terms: 119 + 30.25 = 149.25 30.25 + 11x + x2 = 149.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 149.25 Calculate the square root of the right side: 12.216791723 Break this problem into two subproblems by setting (x + 5.5) equal to 12.216791723 and -12.216791723.Subproblem 1
x + 5.5 = 12.216791723 Simplifying x + 5.5 = 12.216791723 Reorder the terms: 5.5 + x = 12.216791723 Solving 5.5 + x = 12.216791723 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 = 12.216791723 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 12.216791723 + -5.5 x = 12.216791723 + -5.5 Combine like terms: 12.216791723 + -5.5 = 6.716791723 x = 6.716791723 Simplifying x = 6.716791723Subproblem 2
x + 5.5 = -12.216791723 Simplifying x + 5.5 = -12.216791723 Reorder the terms: 5.5 + x = -12.216791723 Solving 5.5 + x = -12.216791723 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 = -12.216791723 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -12.216791723 + -5.5 x = -12.216791723 + -5.5 Combine like terms: -12.216791723 + -5.5 = -17.716791723 x = -17.716791723 Simplifying x = -17.716791723Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.716791723, -17.716791723}
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