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Simplifying 3n2 + 4n + -147 = 0 Reorder the terms: -147 + 4n + 3n2 = 0 Solving -147 + 4n + 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'. -49 + 1.333333333n + n2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + 1.333333333n + 49 + n2 = 0 + 49 Reorder the terms: -49 + 49 + 1.333333333n + n2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 1.333333333n + n2 = 0 + 49 1.333333333n + n2 = 0 + 49 Combine like terms: 0 + 49 = 49 1.333333333n + n2 = 49 The n term is 1.333333333n. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333n + 0.4444444442 + n2 = 49 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333n + n2 = 49 + 0.4444444442 Combine like terms: 49 + 0.4444444442 = 49.4444444442 0.4444444442 + 1.333333333n + n2 = 49.4444444442 Factor a perfect square on the left side: (n + 0.6666666665)(n + 0.6666666665) = 49.4444444442 Calculate the square root of the right side: 7.03167437 Break this problem into two subproblems by setting (n + 0.6666666665) equal to 7.03167437 and -7.03167437.Subproblem 1
n + 0.6666666665 = 7.03167437 Simplifying n + 0.6666666665 = 7.03167437 Reorder the terms: 0.6666666665 + n = 7.03167437 Solving 0.6666666665 + n = 7.03167437 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + n = 7.03167437 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + n = 7.03167437 + -0.6666666665 n = 7.03167437 + -0.6666666665 Combine like terms: 7.03167437 + -0.6666666665 = 6.3650077035 n = 6.3650077035 Simplifying n = 6.3650077035Subproblem 2
n + 0.6666666665 = -7.03167437 Simplifying n + 0.6666666665 = -7.03167437 Reorder the terms: 0.6666666665 + n = -7.03167437 Solving 0.6666666665 + n = -7.03167437 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + n = -7.03167437 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + n = -7.03167437 + -0.6666666665 n = -7.03167437 + -0.6666666665 Combine like terms: -7.03167437 + -0.6666666665 = -7.6983410365 n = -7.6983410365 Simplifying n = -7.6983410365Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.3650077035, -7.6983410365}
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