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Simplifying 11x2 + -32x + -9 = 0 Reorder the terms: -9 + -32x + 11x2 = 0 Solving -9 + -32x + 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'. -0.8181818182 + -2.909090909x + x2 = 0 Move the constant term to the right: Add '0.8181818182' to each side of the equation. -0.8181818182 + -2.909090909x + 0.8181818182 + x2 = 0 + 0.8181818182 Reorder the terms: -0.8181818182 + 0.8181818182 + -2.909090909x + x2 = 0 + 0.8181818182 Combine like terms: -0.8181818182 + 0.8181818182 = 0.0000000000 0.0000000000 + -2.909090909x + x2 = 0 + 0.8181818182 -2.909090909x + x2 = 0 + 0.8181818182 Combine like terms: 0 + 0.8181818182 = 0.8181818182 -2.909090909x + x2 = 0.8181818182 The x term is -2.909090909x. Take half its coefficient (-1.454545455). Square it (2.115702481) and add it to both sides. Add '2.115702481' to each side of the equation. -2.909090909x + 2.115702481 + x2 = 0.8181818182 + 2.115702481 Reorder the terms: 2.115702481 + -2.909090909x + x2 = 0.8181818182 + 2.115702481 Combine like terms: 0.8181818182 + 2.115702481 = 2.9338842992 2.115702481 + -2.909090909x + x2 = 2.9338842992 Factor a perfect square on the left side: (x + -1.454545455)(x + -1.454545455) = 2.9338842992 Calculate the square root of the right side: 1.712858517 Break this problem into two subproblems by setting (x + -1.454545455) equal to 1.712858517 and -1.712858517.Subproblem 1
x + -1.454545455 = 1.712858517 Simplifying x + -1.454545455 = 1.712858517 Reorder the terms: -1.454545455 + x = 1.712858517 Solving -1.454545455 + x = 1.712858517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.454545455' to each side of the equation. -1.454545455 + 1.454545455 + x = 1.712858517 + 1.454545455 Combine like terms: -1.454545455 + 1.454545455 = 0.000000000 0.000000000 + x = 1.712858517 + 1.454545455 x = 1.712858517 + 1.454545455 Combine like terms: 1.712858517 + 1.454545455 = 3.167403972 x = 3.167403972 Simplifying x = 3.167403972Subproblem 2
x + -1.454545455 = -1.712858517 Simplifying x + -1.454545455 = -1.712858517 Reorder the terms: -1.454545455 + x = -1.712858517 Solving -1.454545455 + x = -1.712858517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.454545455' to each side of the equation. -1.454545455 + 1.454545455 + x = -1.712858517 + 1.454545455 Combine like terms: -1.454545455 + 1.454545455 = 0.000000000 0.000000000 + x = -1.712858517 + 1.454545455 x = -1.712858517 + 1.454545455 Combine like terms: -1.712858517 + 1.454545455 = -0.258313062 x = -0.258313062 Simplifying x = -0.258313062Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.167403972, -0.258313062}
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