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Simplifying 3n2 + 5n + -30 = 0 Reorder the terms: -30 + 5n + 3n2 = 0 Solving -30 + 5n + 3n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10 + 1.666666667n + n2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 1.666666667n + 10 + n2 = 0 + 10 Reorder the terms: -10 + 10 + 1.666666667n + n2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 1.666666667n + n2 = 0 + 10 1.666666667n + n2 = 0 + 10 Combine like terms: 0 + 10 = 10 1.666666667n + n2 = 10 The n term is 1.666666667n. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667n + 0.6944444447 + n2 = 10 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667n + n2 = 10 + 0.6944444447 Combine like terms: 10 + 0.6944444447 = 10.6944444447 0.6944444447 + 1.666666667n + n2 = 10.6944444447 Factor a perfect square on the left side: (n + 0.8333333335)(n + 0.8333333335) = 10.6944444447 Calculate the square root of the right side: 3.270236145 Break this problem into two subproblems by setting (n + 0.8333333335) equal to 3.270236145 and -3.270236145.Subproblem 1
n + 0.8333333335 = 3.270236145 Simplifying n + 0.8333333335 = 3.270236145 Reorder the terms: 0.8333333335 + n = 3.270236145 Solving 0.8333333335 + n = 3.270236145 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + n = 3.270236145 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + n = 3.270236145 + -0.8333333335 n = 3.270236145 + -0.8333333335 Combine like terms: 3.270236145 + -0.8333333335 = 2.4369028115 n = 2.4369028115 Simplifying n = 2.4369028115Subproblem 2
n + 0.8333333335 = -3.270236145 Simplifying n + 0.8333333335 = -3.270236145 Reorder the terms: 0.8333333335 + n = -3.270236145 Solving 0.8333333335 + n = -3.270236145 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + n = -3.270236145 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + n = -3.270236145 + -0.8333333335 n = -3.270236145 + -0.8333333335 Combine like terms: -3.270236145 + -0.8333333335 = -4.1035694785 n = -4.1035694785 Simplifying n = -4.1035694785Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.4369028115, -4.1035694785}
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