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Simplifying 169x2 + -182x + -61 = 0 Reorder the terms: -61 + -182x + 169x2 = 0 Solving -61 + -182x + 169x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 169 the coefficient of the squared term: Divide each side by '169'. -0.3609467456 + -1.076923077x + x2 = 0 Move the constant term to the right: Add '0.3609467456' to each side of the equation. -0.3609467456 + -1.076923077x + 0.3609467456 + x2 = 0 + 0.3609467456 Reorder the terms: -0.3609467456 + 0.3609467456 + -1.076923077x + x2 = 0 + 0.3609467456 Combine like terms: -0.3609467456 + 0.3609467456 = 0.0000000000 0.0000000000 + -1.076923077x + x2 = 0 + 0.3609467456 -1.076923077x + x2 = 0 + 0.3609467456 Combine like terms: 0 + 0.3609467456 = 0.3609467456 -1.076923077x + x2 = 0.3609467456 The x term is -1.076923077x. Take half its coefficient (-0.5384615385). Square it (0.2899408284) and add it to both sides. Add '0.2899408284' to each side of the equation. -1.076923077x + 0.2899408284 + x2 = 0.3609467456 + 0.2899408284 Reorder the terms: 0.2899408284 + -1.076923077x + x2 = 0.3609467456 + 0.2899408284 Combine like terms: 0.3609467456 + 0.2899408284 = 0.650887574 0.2899408284 + -1.076923077x + x2 = 0.650887574 Factor a perfect square on the left side: (x + -0.5384615385)(x + -0.5384615385) = 0.650887574 Calculate the square root of the right side: 0.806776037 Break this problem into two subproblems by setting (x + -0.5384615385) equal to 0.806776037 and -0.806776037.Subproblem 1
x + -0.5384615385 = 0.806776037 Simplifying x + -0.5384615385 = 0.806776037 Reorder the terms: -0.5384615385 + x = 0.806776037 Solving -0.5384615385 + x = 0.806776037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5384615385' to each side of the equation. -0.5384615385 + 0.5384615385 + x = 0.806776037 + 0.5384615385 Combine like terms: -0.5384615385 + 0.5384615385 = 0.0000000000 0.0000000000 + x = 0.806776037 + 0.5384615385 x = 0.806776037 + 0.5384615385 Combine like terms: 0.806776037 + 0.5384615385 = 1.3452375755 x = 1.3452375755 Simplifying x = 1.3452375755Subproblem 2
x + -0.5384615385 = -0.806776037 Simplifying x + -0.5384615385 = -0.806776037 Reorder the terms: -0.5384615385 + x = -0.806776037 Solving -0.5384615385 + x = -0.806776037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5384615385' to each side of the equation. -0.5384615385 + 0.5384615385 + x = -0.806776037 + 0.5384615385 Combine like terms: -0.5384615385 + 0.5384615385 = 0.0000000000 0.0000000000 + x = -0.806776037 + 0.5384615385 x = -0.806776037 + 0.5384615385 Combine like terms: -0.806776037 + 0.5384615385 = -0.2683144985 x = -0.2683144985 Simplifying x = -0.2683144985Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3452375755, -0.2683144985}
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