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Simplifying 7n2 = -6n + -1 Reorder the terms: 7n2 = -1 + -6n Solving 7n2 = -1 + -6n Solving for variable 'n'. Reorder the terms: 1 + 6n + 7n2 = -1 + -6n + 1 + 6n Reorder the terms: 1 + 6n + 7n2 = -1 + 1 + -6n + 6n Combine like terms: -1 + 1 = 0 1 + 6n + 7n2 = 0 + -6n + 6n 1 + 6n + 7n2 = -6n + 6n Combine like terms: -6n + 6n = 0 1 + 6n + 7n2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 0.8571428571n + n2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 0.8571428571n + -0.1428571429 + n2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 0.8571428571n + n2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 0.8571428571n + n2 = 0 + -0.1428571429 0.8571428571n + n2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 0.8571428571n + n2 = -0.1428571429 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 = -0.1428571429 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571n + n2 = -0.1428571429 + 0.1836734694 Combine like terms: -0.1428571429 + 0.1836734694 = 0.0408163265 0.1836734694 + 0.8571428571n + n2 = 0.0408163265 Factor a perfect square on the left side: (n + 0.4285714286)(n + 0.4285714286) = 0.0408163265 Calculate the square root of the right side: 0.202030509 Break this problem into two subproblems by setting (n + 0.4285714286) equal to 0.202030509 and -0.202030509.Subproblem 1
n + 0.4285714286 = 0.202030509 Simplifying n + 0.4285714286 = 0.202030509 Reorder the terms: 0.4285714286 + n = 0.202030509 Solving 0.4285714286 + n = 0.202030509 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 = 0.202030509 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + n = 0.202030509 + -0.4285714286 n = 0.202030509 + -0.4285714286 Combine like terms: 0.202030509 + -0.4285714286 = -0.2265409196 n = -0.2265409196 Simplifying n = -0.2265409196Subproblem 2
n + 0.4285714286 = -0.202030509 Simplifying n + 0.4285714286 = -0.202030509 Reorder the terms: 0.4285714286 + n = -0.202030509 Solving 0.4285714286 + n = -0.202030509 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 = -0.202030509 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + n = -0.202030509 + -0.4285714286 n = -0.202030509 + -0.4285714286 Combine like terms: -0.202030509 + -0.4285714286 = -0.6306019376 n = -0.6306019376 Simplifying n = -0.6306019376Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.2265409196, -0.6306019376}
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