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Simplifying 3n2 + 5n + -4 = 2 Reorder the terms: -4 + 5n + 3n2 = 2 Solving -4 + 5n + 3n2 = 2 Solving for variable 'n'. Reorder the terms: -4 + -2 + 5n + 3n2 = 2 + -2 Combine like terms: -4 + -2 = -6 -6 + 5n + 3n2 = 2 + -2 Combine like terms: 2 + -2 = 0 -6 + 5n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + 1.666666667n + n2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.666666667n + 2 + n2 = 0 + 2 Reorder the terms: -2 + 2 + 1.666666667n + n2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.666666667n + n2 = 0 + 2 1.666666667n + n2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.666666667n + n2 = 2 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 = 2 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667n + n2 = 2 + 0.6944444447 Combine like terms: 2 + 0.6944444447 = 2.6944444447 0.6944444447 + 1.666666667n + n2 = 2.6944444447 Factor a perfect square on the left side: (n + 0.8333333335)(n + 0.8333333335) = 2.6944444447 Calculate the square root of the right side: 1.6414763 Break this problem into two subproblems by setting (n + 0.8333333335) equal to 1.6414763 and -1.6414763.Subproblem 1
n + 0.8333333335 = 1.6414763 Simplifying n + 0.8333333335 = 1.6414763 Reorder the terms: 0.8333333335 + n = 1.6414763 Solving 0.8333333335 + n = 1.6414763 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 = 1.6414763 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + n = 1.6414763 + -0.8333333335 n = 1.6414763 + -0.8333333335 Combine like terms: 1.6414763 + -0.8333333335 = 0.8081429665 n = 0.8081429665 Simplifying n = 0.8081429665Subproblem 2
n + 0.8333333335 = -1.6414763 Simplifying n + 0.8333333335 = -1.6414763 Reorder the terms: 0.8333333335 + n = -1.6414763 Solving 0.8333333335 + n = -1.6414763 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 = -1.6414763 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + n = -1.6414763 + -0.8333333335 n = -1.6414763 + -0.8333333335 Combine like terms: -1.6414763 + -0.8333333335 = -2.4748096335 n = -2.4748096335 Simplifying n = -2.4748096335Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.8081429665, -2.4748096335}
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