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Simplifying 7x2 + 13x + 1 = 0 Reorder the terms: 1 + 13x + 7x2 = 0 Solving 1 + 13x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 1.857142857x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 1.857142857x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 1.857142857x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 1.857142857x + x2 = 0 + -0.1428571429 1.857142857x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 1.857142857x + x2 = -0.1428571429 The x term is 1.857142857x. Take half its coefficient (0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. 1.857142857x + 0.8622448978 + x2 = -0.1428571429 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857x + x2 = -0.1428571429 + 0.8622448978 Combine like terms: -0.1428571429 + 0.8622448978 = 0.7193877549 0.8622448978 + 1.857142857x + x2 = 0.7193877549 Factor a perfect square on the left side: (x + 0.9285714285)(x + 0.9285714285) = 0.7193877549 Calculate the square root of the right side: 0.848167292 Break this problem into two subproblems by setting (x + 0.9285714285) equal to 0.848167292 and -0.848167292.Subproblem 1
x + 0.9285714285 = 0.848167292 Simplifying x + 0.9285714285 = 0.848167292 Reorder the terms: 0.9285714285 + x = 0.848167292 Solving 0.9285714285 + x = 0.848167292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + x = 0.848167292 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = 0.848167292 + -0.9285714285 x = 0.848167292 + -0.9285714285 Combine like terms: 0.848167292 + -0.9285714285 = -0.0804041365 x = -0.0804041365 Simplifying x = -0.0804041365Subproblem 2
x + 0.9285714285 = -0.848167292 Simplifying x + 0.9285714285 = -0.848167292 Reorder the terms: 0.9285714285 + x = -0.848167292 Solving 0.9285714285 + x = -0.848167292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + x = -0.848167292 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = -0.848167292 + -0.9285714285 x = -0.848167292 + -0.9285714285 Combine like terms: -0.848167292 + -0.9285714285 = -1.7767387205 x = -1.7767387205 Simplifying x = -1.7767387205Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0804041365, -1.7767387205}
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