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Simplifying 19x2 + -6x + -19 = 0 Reorder the terms: -19 + -6x + 19x2 = 0 Solving -19 + -6x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -1 + -0.3157894737x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.3157894737x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.3157894737x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.3157894737x + x2 = 0 + 1 -0.3157894737x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.3157894737x + x2 = 1 The x term is -0.3157894737x. Take half its coefficient (-0.1578947369). Square it (0.02493074794) and add it to both sides. Add '0.02493074794' to each side of the equation. -0.3157894737x + 0.02493074794 + x2 = 1 + 0.02493074794 Reorder the terms: 0.02493074794 + -0.3157894737x + x2 = 1 + 0.02493074794 Combine like terms: 1 + 0.02493074794 = 1.02493074794 0.02493074794 + -0.3157894737x + x2 = 1.02493074794 Factor a perfect square on the left side: (x + -0.1578947369)(x + -0.1578947369) = 1.02493074794 Calculate the square root of the right side: 1.012388635 Break this problem into two subproblems by setting (x + -0.1578947369) equal to 1.012388635 and -1.012388635.Subproblem 1
x + -0.1578947369 = 1.012388635 Simplifying x + -0.1578947369 = 1.012388635 Reorder the terms: -0.1578947369 + x = 1.012388635 Solving -0.1578947369 + x = 1.012388635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1578947369' to each side of the equation. -0.1578947369 + 0.1578947369 + x = 1.012388635 + 0.1578947369 Combine like terms: -0.1578947369 + 0.1578947369 = 0.0000000000 0.0000000000 + x = 1.012388635 + 0.1578947369 x = 1.012388635 + 0.1578947369 Combine like terms: 1.012388635 + 0.1578947369 = 1.1702833719 x = 1.1702833719 Simplifying x = 1.1702833719Subproblem 2
x + -0.1578947369 = -1.012388635 Simplifying x + -0.1578947369 = -1.012388635 Reorder the terms: -0.1578947369 + x = -1.012388635 Solving -0.1578947369 + x = -1.012388635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1578947369' to each side of the equation. -0.1578947369 + 0.1578947369 + x = -1.012388635 + 0.1578947369 Combine like terms: -0.1578947369 + 0.1578947369 = 0.0000000000 0.0000000000 + x = -1.012388635 + 0.1578947369 x = -1.012388635 + 0.1578947369 Combine like terms: -1.012388635 + 0.1578947369 = -0.8544938981 x = -0.8544938981 Simplifying x = -0.8544938981Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1702833719, -0.8544938981}
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