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Simplifying 7n2 + 6n + -30 = 0 Reorder the terms: -30 + 6n + 7n2 = 0 Solving -30 + 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'. -4.285714286 + 0.8571428571n + n2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + 0.8571428571n + 4.285714286 + n2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + 0.8571428571n + n2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + 0.8571428571n + n2 = 0 + 4.285714286 0.8571428571n + n2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 0.8571428571n + n2 = 4.285714286 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 = 4.285714286 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571n + n2 = 4.285714286 + 0.1836734694 Combine like terms: 4.285714286 + 0.1836734694 = 4.4693877554 0.1836734694 + 0.8571428571n + n2 = 4.4693877554 Factor a perfect square on the left side: (n + 0.4285714286)(n + 0.4285714286) = 4.4693877554 Calculate the square root of the right side: 2.114092655 Break this problem into two subproblems by setting (n + 0.4285714286) equal to 2.114092655 and -2.114092655.Subproblem 1
n + 0.4285714286 = 2.114092655 Simplifying n + 0.4285714286 = 2.114092655 Reorder the terms: 0.4285714286 + n = 2.114092655 Solving 0.4285714286 + n = 2.114092655 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 = 2.114092655 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + n = 2.114092655 + -0.4285714286 n = 2.114092655 + -0.4285714286 Combine like terms: 2.114092655 + -0.4285714286 = 1.6855212264 n = 1.6855212264 Simplifying n = 1.6855212264Subproblem 2
n + 0.4285714286 = -2.114092655 Simplifying n + 0.4285714286 = -2.114092655 Reorder the terms: 0.4285714286 + n = -2.114092655 Solving 0.4285714286 + n = -2.114092655 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 = -2.114092655 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + n = -2.114092655 + -0.4285714286 n = -2.114092655 + -0.4285714286 Combine like terms: -2.114092655 + -0.4285714286 = -2.5426640836 n = -2.5426640836 Simplifying n = -2.5426640836Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.6855212264, -2.5426640836}
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