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Simplifying (11x * 11x) + 3x + -3 = 0 Reorder the terms for easier multiplication: (11 * 11x * x) + 3x + -3 = 0 Multiply 11 * 11 (121x * x) + 3x + -3 = 0 Multiply x * x (121x2) + 3x + -3 = 0 Reorder the terms: -3 + 3x + (121x2) = 0 Solving -3 + 3x + (121x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 121 the coefficient of the squared term: Divide each side by '121'. -0.02479338843 + 0.02479338843x + x2 = 0 Move the constant term to the right: Add '0.02479338843' to each side of the equation. -0.02479338843 + 0.02479338843x + 0.02479338843 + x2 = 0 + 0.02479338843 Reorder the terms: -0.02479338843 + 0.02479338843 + 0.02479338843x + x2 = 0 + 0.02479338843 Combine like terms: -0.02479338843 + 0.02479338843 = 0.00000000000 0.00000000000 + 0.02479338843x + x2 = 0 + 0.02479338843 0.02479338843x + x2 = 0 + 0.02479338843 Combine like terms: 0 + 0.02479338843 = 0.02479338843 0.02479338843x + x2 = 0.02479338843 The x term is 0.02479338843x. Take half its coefficient (0.01239669422). Square it (0.0001536780276) and add it to both sides. Add '0.0001536780276' to each side of the equation. 0.02479338843x + 0.0001536780276 + x2 = 0.02479338843 + 0.0001536780276 Reorder the terms: 0.0001536780276 + 0.02479338843x + x2 = 0.02479338843 + 0.0001536780276 Combine like terms: 0.02479338843 + 0.0001536780276 = 0.0249470664576 0.0001536780276 + 0.02479338843x + x2 = 0.0249470664576 Factor a perfect square on the left side: ((x) + 0.01239669422)((x) + 0.01239669422) = 0.0249470664576 Calculate the square root of the right side: 0.157946404 Break this problem into two subproblems by setting ((x) + 0.01239669422) equal to 0.157946404 and -0.157946404.Subproblem 1
(x) + 0.01239669422 = 0.157946404 Simplifying (x) + 0.01239669422 = 0.157946404 x + 0.01239669422 = 0.157946404 Reorder the terms: 0.01239669422 + x = 0.157946404 Solving 0.01239669422 + x = 0.157946404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01239669422' to each side of the equation. 0.01239669422 + -0.01239669422 + x = 0.157946404 + -0.01239669422 Combine like terms: 0.01239669422 + -0.01239669422 = 0.00000000000 0.00000000000 + x = 0.157946404 + -0.01239669422 x = 0.157946404 + -0.01239669422 Combine like terms: 0.157946404 + -0.01239669422 = 0.14554970978 x = 0.14554970978 Simplifying x = 0.14554970978Subproblem 2
(x) + 0.01239669422 = -0.157946404 Simplifying (x) + 0.01239669422 = -0.157946404 x + 0.01239669422 = -0.157946404 Reorder the terms: 0.01239669422 + x = -0.157946404 Solving 0.01239669422 + x = -0.157946404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01239669422' to each side of the equation. 0.01239669422 + -0.01239669422 + x = -0.157946404 + -0.01239669422 Combine like terms: 0.01239669422 + -0.01239669422 = 0.00000000000 0.00000000000 + x = -0.157946404 + -0.01239669422 x = -0.157946404 + -0.01239669422 Combine like terms: -0.157946404 + -0.01239669422 = -0.17034309822 x = -0.17034309822 Simplifying x = -0.17034309822Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.14554970978, -0.17034309822}
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