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Simplifying 7n2 + -6n + -7 = 0 Reorder the terms: -7 + -6n + 7n2 = 0 Solving -7 + -6n + 7n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + -0.8571428571n + n2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.8571428571n + 1 + n2 = 0 + 1 Reorder the terms: -1 + 1 + -0.8571428571n + n2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.8571428571n + n2 = 0 + 1 -0.8571428571n + n2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.8571428571n + n2 = 1 The n term is -0.8571428571n. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571n + 0.1836734694 + n2 = 1 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571n + n2 = 1 + 0.1836734694 Combine like terms: 1 + 0.1836734694 = 1.1836734694 0.1836734694 + -0.8571428571n + n2 = 1.1836734694 Factor a perfect square on the left side: (n + -0.4285714286)(n + -0.4285714286) = 1.1836734694 Calculate the square root of the right side: 1.087967587 Break this problem into two subproblems by setting (n + -0.4285714286) equal to 1.087967587 and -1.087967587.Subproblem 1
n + -0.4285714286 = 1.087967587 Simplifying n + -0.4285714286 = 1.087967587 Reorder the terms: -0.4285714286 + n = 1.087967587 Solving -0.4285714286 + n = 1.087967587 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + n = 1.087967587 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + n = 1.087967587 + 0.4285714286 n = 1.087967587 + 0.4285714286 Combine like terms: 1.087967587 + 0.4285714286 = 1.5165390156 n = 1.5165390156 Simplifying n = 1.5165390156Subproblem 2
n + -0.4285714286 = -1.087967587 Simplifying n + -0.4285714286 = -1.087967587 Reorder the terms: -0.4285714286 + n = -1.087967587 Solving -0.4285714286 + n = -1.087967587 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + n = -1.087967587 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + n = -1.087967587 + 0.4285714286 n = -1.087967587 + 0.4285714286 Combine like terms: -1.087967587 + 0.4285714286 = -0.6593961584 n = -0.6593961584 Simplifying n = -0.6593961584Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.5165390156, -0.6593961584}
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