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Simplifying -19x2 + -44x + 1 = 0 Reorder the terms: 1 + -44x + -19x2 = 0 Solving 1 + -44x + -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'. -0.05263157895 + 2.315789474x + x2 = 0 Move the constant term to the right: Add '0.05263157895' to each side of the equation. -0.05263157895 + 2.315789474x + 0.05263157895 + x2 = 0 + 0.05263157895 Reorder the terms: -0.05263157895 + 0.05263157895 + 2.315789474x + x2 = 0 + 0.05263157895 Combine like terms: -0.05263157895 + 0.05263157895 = 0.00000000000 0.00000000000 + 2.315789474x + x2 = 0 + 0.05263157895 2.315789474x + x2 = 0 + 0.05263157895 Combine like terms: 0 + 0.05263157895 = 0.05263157895 2.315789474x + x2 = 0.05263157895 The x term is 2.315789474x. Take half its coefficient (1.157894737). Square it (1.340720222) and add it to both sides. Add '1.340720222' to each side of the equation. 2.315789474x + 1.340720222 + x2 = 0.05263157895 + 1.340720222 Reorder the terms: 1.340720222 + 2.315789474x + x2 = 0.05263157895 + 1.340720222 Combine like terms: 0.05263157895 + 1.340720222 = 1.39335180095 1.340720222 + 2.315789474x + x2 = 1.39335180095 Factor a perfect square on the left side: (x + 1.157894737)(x + 1.157894737) = 1.39335180095 Calculate the square root of the right side: 1.180403237 Break this problem into two subproblems by setting (x + 1.157894737) equal to 1.180403237 and -1.180403237.Subproblem 1
x + 1.157894737 = 1.180403237 Simplifying x + 1.157894737 = 1.180403237 Reorder the terms: 1.157894737 + x = 1.180403237 Solving 1.157894737 + x = 1.180403237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.157894737' to each side of the equation. 1.157894737 + -1.157894737 + x = 1.180403237 + -1.157894737 Combine like terms: 1.157894737 + -1.157894737 = 0.000000000 0.000000000 + x = 1.180403237 + -1.157894737 x = 1.180403237 + -1.157894737 Combine like terms: 1.180403237 + -1.157894737 = 0.0225085 x = 0.0225085 Simplifying x = 0.0225085Subproblem 2
x + 1.157894737 = -1.180403237 Simplifying x + 1.157894737 = -1.180403237 Reorder the terms: 1.157894737 + x = -1.180403237 Solving 1.157894737 + x = -1.180403237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.157894737' to each side of the equation. 1.157894737 + -1.157894737 + x = -1.180403237 + -1.157894737 Combine like terms: 1.157894737 + -1.157894737 = 0.000000000 0.000000000 + x = -1.180403237 + -1.157894737 x = -1.180403237 + -1.157894737 Combine like terms: -1.180403237 + -1.157894737 = -2.338297974 x = -2.338297974 Simplifying x = -2.338297974Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0225085, -2.338297974}
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