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Simplifying -3n2 + 4n + 3 = 0 Reorder the terms: 3 + 4n + -3n2 = 0 Solving 3 + 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'. -1 + -1.333333333n + n2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.333333333n + 1 + n2 = 0 + 1 Reorder the terms: -1 + 1 + -1.333333333n + n2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.333333333n + n2 = 0 + 1 -1.333333333n + n2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.333333333n + n2 = 1 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 = 1 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333n + n2 = 1 + 0.4444444442 Combine like terms: 1 + 0.4444444442 = 1.4444444442 0.4444444442 + -1.333333333n + n2 = 1.4444444442 Factor a perfect square on the left side: (n + -0.6666666665)(n + -0.6666666665) = 1.4444444442 Calculate the square root of the right side: 1.201850425 Break this problem into two subproblems by setting (n + -0.6666666665) equal to 1.201850425 and -1.201850425.Subproblem 1
n + -0.6666666665 = 1.201850425 Simplifying n + -0.6666666665 = 1.201850425 Reorder the terms: -0.6666666665 + n = 1.201850425 Solving -0.6666666665 + n = 1.201850425 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 = 1.201850425 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + n = 1.201850425 + 0.6666666665 n = 1.201850425 + 0.6666666665 Combine like terms: 1.201850425 + 0.6666666665 = 1.8685170915 n = 1.8685170915 Simplifying n = 1.8685170915Subproblem 2
n + -0.6666666665 = -1.201850425 Simplifying n + -0.6666666665 = -1.201850425 Reorder the terms: -0.6666666665 + n = -1.201850425 Solving -0.6666666665 + n = -1.201850425 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 = -1.201850425 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + n = -1.201850425 + 0.6666666665 n = -1.201850425 + 0.6666666665 Combine like terms: -1.201850425 + 0.6666666665 = -0.5351837585 n = -0.5351837585 Simplifying n = -0.5351837585Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.8685170915, -0.5351837585}
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