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Simplifying 11x2 + -98x + 120 = 0 Reorder the terms: 120 + -98x + 11x2 = 0 Solving 120 + -98x + 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'. 10.90909091 + -8.909090909x + x2 = 0 Move the constant term to the right: Add '-10.90909091' to each side of the equation. 10.90909091 + -8.909090909x + -10.90909091 + x2 = 0 + -10.90909091 Reorder the terms: 10.90909091 + -10.90909091 + -8.909090909x + x2 = 0 + -10.90909091 Combine like terms: 10.90909091 + -10.90909091 = 0.00000000 0.00000000 + -8.909090909x + x2 = 0 + -10.90909091 -8.909090909x + x2 = 0 + -10.90909091 Combine like terms: 0 + -10.90909091 = -10.90909091 -8.909090909x + x2 = -10.90909091 The x term is -8.909090909x. Take half its coefficient (-4.454545455). Square it (19.84297521) and add it to both sides. Add '19.84297521' to each side of the equation. -8.909090909x + 19.84297521 + x2 = -10.90909091 + 19.84297521 Reorder the terms: 19.84297521 + -8.909090909x + x2 = -10.90909091 + 19.84297521 Combine like terms: -10.90909091 + 19.84297521 = 8.9338843 19.84297521 + -8.909090909x + x2 = 8.9338843 Factor a perfect square on the left side: (x + -4.454545455)(x + -4.454545455) = 8.9338843 Calculate the square root of the right side: 2.988960405 Break this problem into two subproblems by setting (x + -4.454545455) equal to 2.988960405 and -2.988960405.Subproblem 1
x + -4.454545455 = 2.988960405 Simplifying x + -4.454545455 = 2.988960405 Reorder the terms: -4.454545455 + x = 2.988960405 Solving -4.454545455 + x = 2.988960405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.454545455' to each side of the equation. -4.454545455 + 4.454545455 + x = 2.988960405 + 4.454545455 Combine like terms: -4.454545455 + 4.454545455 = 0.000000000 0.000000000 + x = 2.988960405 + 4.454545455 x = 2.988960405 + 4.454545455 Combine like terms: 2.988960405 + 4.454545455 = 7.44350586 x = 7.44350586 Simplifying x = 7.44350586Subproblem 2
x + -4.454545455 = -2.988960405 Simplifying x + -4.454545455 = -2.988960405 Reorder the terms: -4.454545455 + x = -2.988960405 Solving -4.454545455 + x = -2.988960405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.454545455' to each side of the equation. -4.454545455 + 4.454545455 + x = -2.988960405 + 4.454545455 Combine like terms: -4.454545455 + 4.454545455 = 0.000000000 0.000000000 + x = -2.988960405 + 4.454545455 x = -2.988960405 + 4.454545455 Combine like terms: -2.988960405 + 4.454545455 = 1.46558505 x = 1.46558505 Simplifying x = 1.46558505Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.44350586, 1.46558505}
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