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Simplifying 3n2 + -56 = 4 + 20n Reorder the terms: -56 + 3n2 = 4 + 20n Solving -56 + 3n2 = 4 + 20n Solving for variable 'n'. Reorder the terms: -56 + -4 + -20n + 3n2 = 4 + 20n + -4 + -20n Combine like terms: -56 + -4 = -60 -60 + -20n + 3n2 = 4 + 20n + -4 + -20n Reorder the terms: -60 + -20n + 3n2 = 4 + -4 + 20n + -20n Combine like terms: 4 + -4 = 0 -60 + -20n + 3n2 = 0 + 20n + -20n -60 + -20n + 3n2 = 20n + -20n Combine like terms: 20n + -20n = 0 -60 + -20n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -20 + -6.666666667n + n2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -6.666666667n + 20 + n2 = 0 + 20 Reorder the terms: -20 + 20 + -6.666666667n + n2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -6.666666667n + n2 = 0 + 20 -6.666666667n + n2 = 0 + 20 Combine like terms: 0 + 20 = 20 -6.666666667n + n2 = 20 The n term is -6.666666667n. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667n + 11.11111112 + n2 = 20 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667n + n2 = 20 + 11.11111112 Combine like terms: 20 + 11.11111112 = 31.11111112 11.11111112 + -6.666666667n + n2 = 31.11111112 Factor a perfect square on the left side: (n + -3.333333334)(n + -3.333333334) = 31.11111112 Calculate the square root of the right side: 5.577733511 Break this problem into two subproblems by setting (n + -3.333333334) equal to 5.577733511 and -5.577733511.Subproblem 1
n + -3.333333334 = 5.577733511 Simplifying n + -3.333333334 = 5.577733511 Reorder the terms: -3.333333334 + n = 5.577733511 Solving -3.333333334 + n = 5.577733511 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + n = 5.577733511 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + n = 5.577733511 + 3.333333334 n = 5.577733511 + 3.333333334 Combine like terms: 5.577733511 + 3.333333334 = 8.911066845 n = 8.911066845 Simplifying n = 8.911066845Subproblem 2
n + -3.333333334 = -5.577733511 Simplifying n + -3.333333334 = -5.577733511 Reorder the terms: -3.333333334 + n = -5.577733511 Solving -3.333333334 + n = -5.577733511 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + n = -5.577733511 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + n = -5.577733511 + 3.333333334 n = -5.577733511 + 3.333333334 Combine like terms: -5.577733511 + 3.333333334 = -2.244400177 n = -2.244400177 Simplifying n = -2.244400177Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.911066845, -2.244400177}
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