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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 = 1.0051020407 0.8622448978 + -1.857142857x + x2 = 1.0051020407 Factor a perfect square on the left side: (x + -0.9285714285)(x + -0.9285714285) = 1.0051020407 Calculate the square root of the right side: 1.002547775 Break this problem into two subproblems by setting (x + -0.9285714285) equal to 1.002547775 and -1.002547775.Subproblem 1
x + -0.9285714285 = 1.002547775 Simplifying x + -0.9285714285 = 1.002547775 Reorder the terms: -0.9285714285 + x = 1.002547775 Solving -0.9285714285 + x = 1.002547775 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 = 1.002547775 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = 1.002547775 + 0.9285714285 x = 1.002547775 + 0.9285714285 Combine like terms: 1.002547775 + 0.9285714285 = 1.9311192035 x = 1.9311192035 Simplifying x = 1.9311192035Subproblem 2
x + -0.9285714285 = -1.002547775 Simplifying x + -0.9285714285 = -1.002547775 Reorder the terms: -0.9285714285 + x = -1.002547775 Solving -0.9285714285 + x = -1.002547775 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 = -1.002547775 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = -1.002547775 + 0.9285714285 x = -1.002547775 + 0.9285714285 Combine like terms: -1.002547775 + 0.9285714285 = -0.0739763465 x = -0.0739763465 Simplifying x = -0.0739763465Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9311192035, -0.0739763465}
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