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Simplifying 9n2 + 39n = 37 Reorder the terms: 39n + 9n2 = 37 Solving 39n + 9n2 = 37 Solving for variable 'n'. Reorder the terms: -37 + 39n + 9n2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + 39n + 9n2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -4.111111111 + 4.333333333n + n2 = 0 Move the constant term to the right: Add '4.111111111' to each side of the equation. -4.111111111 + 4.333333333n + 4.111111111 + n2 = 0 + 4.111111111 Reorder the terms: -4.111111111 + 4.111111111 + 4.333333333n + n2 = 0 + 4.111111111 Combine like terms: -4.111111111 + 4.111111111 = 0.000000000 0.000000000 + 4.333333333n + n2 = 0 + 4.111111111 4.333333333n + n2 = 0 + 4.111111111 Combine like terms: 0 + 4.111111111 = 4.111111111 4.333333333n + n2 = 4.111111111 The n term is 4.333333333n. Take half its coefficient (2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. 4.333333333n + 4.694444446 + n2 = 4.111111111 + 4.694444446 Reorder the terms: 4.694444446 + 4.333333333n + n2 = 4.111111111 + 4.694444446 Combine like terms: 4.111111111 + 4.694444446 = 8.805555557 4.694444446 + 4.333333333n + n2 = 8.805555557 Factor a perfect square on the left side: (n + 2.166666667)(n + 2.166666667) = 8.805555557 Calculate the square root of the right side: 2.967415636 Break this problem into two subproblems by setting (n + 2.166666667) equal to 2.967415636 and -2.967415636.Subproblem 1
n + 2.166666667 = 2.967415636 Simplifying n + 2.166666667 = 2.967415636 Reorder the terms: 2.166666667 + n = 2.967415636 Solving 2.166666667 + n = 2.967415636 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + n = 2.967415636 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + n = 2.967415636 + -2.166666667 n = 2.967415636 + -2.166666667 Combine like terms: 2.967415636 + -2.166666667 = 0.800748969 n = 0.800748969 Simplifying n = 0.800748969Subproblem 2
n + 2.166666667 = -2.967415636 Simplifying n + 2.166666667 = -2.967415636 Reorder the terms: 2.166666667 + n = -2.967415636 Solving 2.166666667 + n = -2.967415636 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + n = -2.967415636 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + n = -2.967415636 + -2.166666667 n = -2.967415636 + -2.166666667 Combine like terms: -2.967415636 + -2.166666667 = -5.134082303 n = -5.134082303 Simplifying n = -5.134082303Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.800748969, -5.134082303}
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