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Simplifying 11x2 + -9x + -5 = 0 Reorder the terms: -5 + -9x + 11x2 = 0 Solving -5 + -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'. -0.4545454545 + -0.8181818182x + x2 = 0 Move the constant term to the right: Add '0.4545454545' to each side of the equation. -0.4545454545 + -0.8181818182x + 0.4545454545 + x2 = 0 + 0.4545454545 Reorder the terms: -0.4545454545 + 0.4545454545 + -0.8181818182x + x2 = 0 + 0.4545454545 Combine like terms: -0.4545454545 + 0.4545454545 = 0.0000000000 0.0000000000 + -0.8181818182x + x2 = 0 + 0.4545454545 -0.8181818182x + x2 = 0 + 0.4545454545 Combine like terms: 0 + 0.4545454545 = 0.4545454545 -0.8181818182x + x2 = 0.4545454545 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 = 0.4545454545 + 0.1673553719 Reorder the terms: 0.1673553719 + -0.8181818182x + x2 = 0.4545454545 + 0.1673553719 Combine like terms: 0.4545454545 + 0.1673553719 = 0.6219008264 0.1673553719 + -0.8181818182x + x2 = 0.6219008264 Factor a perfect square on the left side: (x + -0.4090909091)(x + -0.4090909091) = 0.6219008264 Calculate the square root of the right side: 0.78860689 Break this problem into two subproblems by setting (x + -0.4090909091) equal to 0.78860689 and -0.78860689.Subproblem 1
x + -0.4090909091 = 0.78860689 Simplifying x + -0.4090909091 = 0.78860689 Reorder the terms: -0.4090909091 + x = 0.78860689 Solving -0.4090909091 + x = 0.78860689 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 = 0.78860689 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + x = 0.78860689 + 0.4090909091 x = 0.78860689 + 0.4090909091 Combine like terms: 0.78860689 + 0.4090909091 = 1.1976977991 x = 1.1976977991 Simplifying x = 1.1976977991Subproblem 2
x + -0.4090909091 = -0.78860689 Simplifying x + -0.4090909091 = -0.78860689 Reorder the terms: -0.4090909091 + x = -0.78860689 Solving -0.4090909091 + x = -0.78860689 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 = -0.78860689 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + x = -0.78860689 + 0.4090909091 x = -0.78860689 + 0.4090909091 Combine like terms: -0.78860689 + 0.4090909091 = -0.3795159809 x = -0.3795159809 Simplifying x = -0.3795159809Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1976977991, -0.3795159809}
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