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Simplifying 11x2 + -9x + -11 = 0 Reorder the terms: -11 + -9x + 11x2 = 0 Solving -11 + -9x + 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'. -1 + -0.8181818182x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.8181818182x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.8181818182x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.8181818182x + x2 = 0 + 1 -0.8181818182x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.8181818182x + x2 = 1 The x term is -0.8181818182x. Take half its coefficient (-0.4090909091). Square it (0.1673553719) and add it to both sides. Add '0.1673553719' to each side of the equation. -0.8181818182x + 0.1673553719 + x2 = 1 + 0.1673553719 Reorder the terms: 0.1673553719 + -0.8181818182x + x2 = 1 + 0.1673553719 Combine like terms: 1 + 0.1673553719 = 1.1673553719 0.1673553719 + -0.8181818182x + x2 = 1.1673553719 Factor a perfect square on the left side: (x + -0.4090909091)(x + -0.4090909091) = 1.1673553719 Calculate the square root of the right side: 1.080442211 Break this problem into two subproblems by setting (x + -0.4090909091) equal to 1.080442211 and -1.080442211.Subproblem 1
x + -0.4090909091 = 1.080442211 Simplifying x + -0.4090909091 = 1.080442211 Reorder the terms: -0.4090909091 + x = 1.080442211 Solving -0.4090909091 + x = 1.080442211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4090909091' to each side of the equation. -0.4090909091 + 0.4090909091 + x = 1.080442211 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + x = 1.080442211 + 0.4090909091 x = 1.080442211 + 0.4090909091 Combine like terms: 1.080442211 + 0.4090909091 = 1.4895331201 x = 1.4895331201 Simplifying x = 1.4895331201Subproblem 2
x + -0.4090909091 = -1.080442211 Simplifying x + -0.4090909091 = -1.080442211 Reorder the terms: -0.4090909091 + x = -1.080442211 Solving -0.4090909091 + x = -1.080442211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4090909091' to each side of the equation. -0.4090909091 + 0.4090909091 + x = -1.080442211 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + x = -1.080442211 + 0.4090909091 x = -1.080442211 + 0.4090909091 Combine like terms: -1.080442211 + 0.4090909091 = -0.6713513019 x = -0.6713513019 Simplifying x = -0.6713513019Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4895331201, -0.6713513019}
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