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Simplifying 11x2 = 1 + 9x Solving 11x2 = 1 + 9x Solving for variable 'x'. Reorder the terms: -1 + -9x + 11x2 = 1 + 9x + -1 + -9x Reorder the terms: -1 + -9x + 11x2 = 1 + -1 + 9x + -9x Combine like terms: 1 + -1 = 0 -1 + -9x + 11x2 = 0 + 9x + -9x -1 + -9x + 11x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -1 + -9x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.09090909091 + -0.8181818182x + x2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + -0.8181818182x + 0.09090909091 + x2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + -0.8181818182x + x2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + -0.8181818182x + x2 = 0 + 0.09090909091 -0.8181818182x + x2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 -0.8181818182x + x2 = 0.09090909091 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 = 0.09090909091 + 0.1673553719 Reorder the terms: 0.1673553719 + -0.8181818182x + x2 = 0.09090909091 + 0.1673553719 Combine like terms: 0.09090909091 + 0.1673553719 = 0.25826446281 0.1673553719 + -0.8181818182x + x2 = 0.25826446281 Factor a perfect square on the left side: (x + -0.4090909091)(x + -0.4090909091) = 0.25826446281 Calculate the square root of the right side: 0.508197268 Break this problem into two subproblems by setting (x + -0.4090909091) equal to 0.508197268 and -0.508197268.Subproblem 1
x + -0.4090909091 = 0.508197268 Simplifying x + -0.4090909091 = 0.508197268 Reorder the terms: -0.4090909091 + x = 0.508197268 Solving -0.4090909091 + x = 0.508197268 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 = 0.508197268 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + x = 0.508197268 + 0.4090909091 x = 0.508197268 + 0.4090909091 Combine like terms: 0.508197268 + 0.4090909091 = 0.9172881771 x = 0.9172881771 Simplifying x = 0.9172881771Subproblem 2
x + -0.4090909091 = -0.508197268 Simplifying x + -0.4090909091 = -0.508197268 Reorder the terms: -0.4090909091 + x = -0.508197268 Solving -0.4090909091 + x = -0.508197268 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 = -0.508197268 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + x = -0.508197268 + 0.4090909091 x = -0.508197268 + 0.4090909091 Combine like terms: -0.508197268 + 0.4090909091 = -0.0991063589 x = -0.0991063589 Simplifying x = -0.0991063589Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9172881771, -0.0991063589}
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