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Simplifying 7x2 + 13x + -38 = 0 Reorder the terms: -38 + 13x + 7x2 = 0 Solving -38 + 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'. -5.428571429 + 1.857142857x + x2 = 0 Move the constant term to the right: Add '5.428571429' to each side of the equation. -5.428571429 + 1.857142857x + 5.428571429 + x2 = 0 + 5.428571429 Reorder the terms: -5.428571429 + 5.428571429 + 1.857142857x + x2 = 0 + 5.428571429 Combine like terms: -5.428571429 + 5.428571429 = 0.000000000 0.000000000 + 1.857142857x + x2 = 0 + 5.428571429 1.857142857x + x2 = 0 + 5.428571429 Combine like terms: 0 + 5.428571429 = 5.428571429 1.857142857x + x2 = 5.428571429 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 = 5.428571429 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857x + x2 = 5.428571429 + 0.8622448978 Combine like terms: 5.428571429 + 0.8622448978 = 6.2908163268 0.8622448978 + 1.857142857x + x2 = 6.2908163268 Factor a perfect square on the left side: (x + 0.9285714285)(x + 0.9285714285) = 6.2908163268 Calculate the square root of the right side: 2.508149981 Break this problem into two subproblems by setting (x + 0.9285714285) equal to 2.508149981 and -2.508149981.Subproblem 1
x + 0.9285714285 = 2.508149981 Simplifying x + 0.9285714285 = 2.508149981 Reorder the terms: 0.9285714285 + x = 2.508149981 Solving 0.9285714285 + x = 2.508149981 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 = 2.508149981 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = 2.508149981 + -0.9285714285 x = 2.508149981 + -0.9285714285 Combine like terms: 2.508149981 + -0.9285714285 = 1.5795785525 x = 1.5795785525 Simplifying x = 1.5795785525Subproblem 2
x + 0.9285714285 = -2.508149981 Simplifying x + 0.9285714285 = -2.508149981 Reorder the terms: 0.9285714285 + x = -2.508149981 Solving 0.9285714285 + x = -2.508149981 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 = -2.508149981 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = -2.508149981 + -0.9285714285 x = -2.508149981 + -0.9285714285 Combine like terms: -2.508149981 + -0.9285714285 = -3.4367214095 x = -3.4367214095 Simplifying x = -3.4367214095Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5795785525, -3.4367214095}
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