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Simplifying 361x2 + -38x + -1 = 0 Reorder the terms: -1 + -38x + 361x2 = 0 Solving -1 + -38x + 361x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 361 the coefficient of the squared term: Divide each side by '361'. -0.002770083102 + -0.1052631579x + x2 = 0 Move the constant term to the right: Add '0.002770083102' to each side of the equation. -0.002770083102 + -0.1052631579x + 0.002770083102 + x2 = 0 + 0.002770083102 Reorder the terms: -0.002770083102 + 0.002770083102 + -0.1052631579x + x2 = 0 + 0.002770083102 Combine like terms: -0.002770083102 + 0.002770083102 = 0.000000000000 0.000000000000 + -0.1052631579x + x2 = 0 + 0.002770083102 -0.1052631579x + x2 = 0 + 0.002770083102 Combine like terms: 0 + 0.002770083102 = 0.002770083102 -0.1052631579x + x2 = 0.002770083102 The x term is -0.1052631579x. Take half its coefficient (-0.05263157895). Square it (0.002770083103) and add it to both sides. Add '0.002770083103' to each side of the equation. -0.1052631579x + 0.002770083103 + x2 = 0.002770083102 + 0.002770083103 Reorder the terms: 0.002770083103 + -0.1052631579x + x2 = 0.002770083102 + 0.002770083103 Combine like terms: 0.002770083102 + 0.002770083103 = 0.005540166205 0.002770083103 + -0.1052631579x + x2 = 0.005540166205 Factor a perfect square on the left side: (x + -0.05263157895)(x + -0.05263157895) = 0.005540166205 Calculate the square root of the right side: 0.074432293 Break this problem into two subproblems by setting (x + -0.05263157895) equal to 0.074432293 and -0.074432293.Subproblem 1
x + -0.05263157895 = 0.074432293 Simplifying x + -0.05263157895 = 0.074432293 Reorder the terms: -0.05263157895 + x = 0.074432293 Solving -0.05263157895 + x = 0.074432293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05263157895' to each side of the equation. -0.05263157895 + 0.05263157895 + x = 0.074432293 + 0.05263157895 Combine like terms: -0.05263157895 + 0.05263157895 = 0.00000000000 0.00000000000 + x = 0.074432293 + 0.05263157895 x = 0.074432293 + 0.05263157895 Combine like terms: 0.074432293 + 0.05263157895 = 0.12706387195 x = 0.12706387195 Simplifying x = 0.12706387195Subproblem 2
x + -0.05263157895 = -0.074432293 Simplifying x + -0.05263157895 = -0.074432293 Reorder the terms: -0.05263157895 + x = -0.074432293 Solving -0.05263157895 + x = -0.074432293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05263157895' to each side of the equation. -0.05263157895 + 0.05263157895 + x = -0.074432293 + 0.05263157895 Combine like terms: -0.05263157895 + 0.05263157895 = 0.00000000000 0.00000000000 + x = -0.074432293 + 0.05263157895 x = -0.074432293 + 0.05263157895 Combine like terms: -0.074432293 + 0.05263157895 = -0.02180071405 x = -0.02180071405 Simplifying x = -0.02180071405Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.12706387195, -0.02180071405}
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