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Simplifying x2 + -11x + -121 = 0 Reorder the terms: -121 + -11x + x2 = 0 Solving -121 + -11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '121' to each side of the equation. -121 + -11x + 121 + x2 = 0 + 121 Reorder the terms: -121 + 121 + -11x + x2 = 0 + 121 Combine like terms: -121 + 121 = 0 0 + -11x + x2 = 0 + 121 -11x + x2 = 0 + 121 Combine like terms: 0 + 121 = 121 -11x + x2 = 121 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 = 121 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 121 + 30.25 Combine like terms: 121 + 30.25 = 151.25 30.25 + -11x + x2 = 151.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 151.25 Calculate the square root of the right side: 12.298373876 Break this problem into two subproblems by setting (x + -5.5) equal to 12.298373876 and -12.298373876.Subproblem 1
x + -5.5 = 12.298373876 Simplifying x + -5.5 = 12.298373876 Reorder the terms: -5.5 + x = 12.298373876 Solving -5.5 + x = 12.298373876 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 = 12.298373876 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 12.298373876 + 5.5 x = 12.298373876 + 5.5 Combine like terms: 12.298373876 + 5.5 = 17.798373876 x = 17.798373876 Simplifying x = 17.798373876Subproblem 2
x + -5.5 = -12.298373876 Simplifying x + -5.5 = -12.298373876 Reorder the terms: -5.5 + x = -12.298373876 Solving -5.5 + x = -12.298373876 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 = -12.298373876 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -12.298373876 + 5.5 x = -12.298373876 + 5.5 Combine like terms: -12.298373876 + 5.5 = -6.798373876 x = -6.798373876 Simplifying x = -6.798373876Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.798373876, -6.798373876}
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