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Simplifying 11x2 + 141x + -108 = 0 Reorder the terms: -108 + 141x + 11x2 = 0 Solving -108 + 141x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -9.818181818 + 12.81818182x + x2 = 0 Move the constant term to the right: Add '9.818181818' to each side of the equation. -9.818181818 + 12.81818182x + 9.818181818 + x2 = 0 + 9.818181818 Reorder the terms: -9.818181818 + 9.818181818 + 12.81818182x + x2 = 0 + 9.818181818 Combine like terms: -9.818181818 + 9.818181818 = 0.000000000 0.000000000 + 12.81818182x + x2 = 0 + 9.818181818 12.81818182x + x2 = 0 + 9.818181818 Combine like terms: 0 + 9.818181818 = 9.818181818 12.81818182x + x2 = 9.818181818 The x term is 12.81818182x. Take half its coefficient (6.40909091). Square it (41.07644629) and add it to both sides. Add '41.07644629' to each side of the equation. 12.81818182x + 41.07644629 + x2 = 9.818181818 + 41.07644629 Reorder the terms: 41.07644629 + 12.81818182x + x2 = 9.818181818 + 41.07644629 Combine like terms: 9.818181818 + 41.07644629 = 50.894628108 41.07644629 + 12.81818182x + x2 = 50.894628108 Factor a perfect square on the left side: (x + 6.40909091)(x + 6.40909091) = 50.894628108 Calculate the square root of the right side: 7.134047106 Break this problem into two subproblems by setting (x + 6.40909091) equal to 7.134047106 and -7.134047106.Subproblem 1
x + 6.40909091 = 7.134047106 Simplifying x + 6.40909091 = 7.134047106 Reorder the terms: 6.40909091 + x = 7.134047106 Solving 6.40909091 + x = 7.134047106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.40909091' to each side of the equation. 6.40909091 + -6.40909091 + x = 7.134047106 + -6.40909091 Combine like terms: 6.40909091 + -6.40909091 = 0.00000000 0.00000000 + x = 7.134047106 + -6.40909091 x = 7.134047106 + -6.40909091 Combine like terms: 7.134047106 + -6.40909091 = 0.724956196 x = 0.724956196 Simplifying x = 0.724956196Subproblem 2
x + 6.40909091 = -7.134047106 Simplifying x + 6.40909091 = -7.134047106 Reorder the terms: 6.40909091 + x = -7.134047106 Solving 6.40909091 + x = -7.134047106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.40909091' to each side of the equation. 6.40909091 + -6.40909091 + x = -7.134047106 + -6.40909091 Combine like terms: 6.40909091 + -6.40909091 = 0.00000000 0.00000000 + x = -7.134047106 + -6.40909091 x = -7.134047106 + -6.40909091 Combine like terms: -7.134047106 + -6.40909091 = -13.543138016 x = -13.543138016 Simplifying x = -13.543138016Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.724956196, -13.543138016}
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