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Simplifying 11x2 + 18x + -2179 = 0 Reorder the terms: -2179 + 18x + 11x2 = 0 Solving -2179 + 18x + 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'. -198.0909091 + 1.636363636x + x2 = 0 Move the constant term to the right: Add '198.0909091' to each side of the equation. -198.0909091 + 1.636363636x + 198.0909091 + x2 = 0 + 198.0909091 Reorder the terms: -198.0909091 + 198.0909091 + 1.636363636x + x2 = 0 + 198.0909091 Combine like terms: -198.0909091 + 198.0909091 = 0.0000000 0.0000000 + 1.636363636x + x2 = 0 + 198.0909091 1.636363636x + x2 = 0 + 198.0909091 Combine like terms: 0 + 198.0909091 = 198.0909091 1.636363636x + x2 = 198.0909091 The x term is 1.636363636x. Take half its coefficient (0.818181818). Square it (0.6694214873) and add it to both sides. Add '0.6694214873' to each side of the equation. 1.636363636x + 0.6694214873 + x2 = 198.0909091 + 0.6694214873 Reorder the terms: 0.6694214873 + 1.636363636x + x2 = 198.0909091 + 0.6694214873 Combine like terms: 198.0909091 + 0.6694214873 = 198.7603305873 0.6694214873 + 1.636363636x + x2 = 198.7603305873 Factor a perfect square on the left side: (x + 0.818181818)(x + 0.818181818) = 198.7603305873 Calculate the square root of the right side: 14.098238563 Break this problem into two subproblems by setting (x + 0.818181818) equal to 14.098238563 and -14.098238563.Subproblem 1
x + 0.818181818 = 14.098238563 Simplifying x + 0.818181818 = 14.098238563 Reorder the terms: 0.818181818 + x = 14.098238563 Solving 0.818181818 + x = 14.098238563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.818181818' to each side of the equation. 0.818181818 + -0.818181818 + x = 14.098238563 + -0.818181818 Combine like terms: 0.818181818 + -0.818181818 = 0.000000000 0.000000000 + x = 14.098238563 + -0.818181818 x = 14.098238563 + -0.818181818 Combine like terms: 14.098238563 + -0.818181818 = 13.280056745 x = 13.280056745 Simplifying x = 13.280056745Subproblem 2
x + 0.818181818 = -14.098238563 Simplifying x + 0.818181818 = -14.098238563 Reorder the terms: 0.818181818 + x = -14.098238563 Solving 0.818181818 + x = -14.098238563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.818181818' to each side of the equation. 0.818181818 + -0.818181818 + x = -14.098238563 + -0.818181818 Combine like terms: 0.818181818 + -0.818181818 = 0.000000000 0.000000000 + x = -14.098238563 + -0.818181818 x = -14.098238563 + -0.818181818 Combine like terms: -14.098238563 + -0.818181818 = -14.916420381 x = -14.916420381 Simplifying x = -14.916420381Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.280056745, -14.916420381}
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