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Simplifying -49n2 + 28n + 4 = 0 Reorder the terms: 4 + 28n + -49n2 = 0 Solving 4 + 28n + -49n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -49 the coefficient of the squared term: Divide each side by '-49'. -0.08163265306 + -0.5714285714n + n2 = 0 Move the constant term to the right: Add '0.08163265306' to each side of the equation. -0.08163265306 + -0.5714285714n + 0.08163265306 + n2 = 0 + 0.08163265306 Reorder the terms: -0.08163265306 + 0.08163265306 + -0.5714285714n + n2 = 0 + 0.08163265306 Combine like terms: -0.08163265306 + 0.08163265306 = 0.00000000000 0.00000000000 + -0.5714285714n + n2 = 0 + 0.08163265306 -0.5714285714n + n2 = 0 + 0.08163265306 Combine like terms: 0 + 0.08163265306 = 0.08163265306 -0.5714285714n + n2 = 0.08163265306 The n term is -0.5714285714n. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714n + 0.08163265305 + n2 = 0.08163265306 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714n + n2 = 0.08163265306 + 0.08163265305 Combine like terms: 0.08163265306 + 0.08163265305 = 0.16326530611 0.08163265305 + -0.5714285714n + n2 = 0.16326530611 Factor a perfect square on the left side: (n + -0.2857142857)(n + -0.2857142857) = 0.16326530611 Calculate the square root of the right side: 0.404061018 Break this problem into two subproblems by setting (n + -0.2857142857) equal to 0.404061018 and -0.404061018.Subproblem 1
n + -0.2857142857 = 0.404061018 Simplifying n + -0.2857142857 = 0.404061018 Reorder the terms: -0.2857142857 + n = 0.404061018 Solving -0.2857142857 + n = 0.404061018 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + n = 0.404061018 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + n = 0.404061018 + 0.2857142857 n = 0.404061018 + 0.2857142857 Combine like terms: 0.404061018 + 0.2857142857 = 0.6897753037 n = 0.6897753037 Simplifying n = 0.6897753037Subproblem 2
n + -0.2857142857 = -0.404061018 Simplifying n + -0.2857142857 = -0.404061018 Reorder the terms: -0.2857142857 + n = -0.404061018 Solving -0.2857142857 + n = -0.404061018 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + n = -0.404061018 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + n = -0.404061018 + 0.2857142857 n = -0.404061018 + 0.2857142857 Combine like terms: -0.404061018 + 0.2857142857 = -0.1183467323 n = -0.1183467323 Simplifying n = -0.1183467323Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.6897753037, -0.1183467323}
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