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Simplifying 0 = n2 + -4n + -168 Reorder the terms: 0 = -168 + -4n + n2 Solving 0 = -168 + -4n + n2 Solving for variable 'n'. Combine like terms: 0 + 168 = 168 168 + 4n + -1n2 = -168 + -4n + n2 + 168 + 4n + -1n2 Reorder the terms: 168 + 4n + -1n2 = -168 + 168 + -4n + 4n + n2 + -1n2 Combine like terms: -168 + 168 = 0 168 + 4n + -1n2 = 0 + -4n + 4n + n2 + -1n2 168 + 4n + -1n2 = -4n + 4n + n2 + -1n2 Combine like terms: -4n + 4n = 0 168 + 4n + -1n2 = 0 + n2 + -1n2 168 + 4n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 168 + 4n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -168 + -4n + n2 = 0 Move the constant term to the right: Add '168' to each side of the equation. -168 + -4n + 168 + n2 = 0 + 168 Reorder the terms: -168 + 168 + -4n + n2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + -4n + n2 = 0 + 168 -4n + n2 = 0 + 168 Combine like terms: 0 + 168 = 168 -4n + n2 = 168 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 168 + 4 Reorder the terms: 4 + -4n + n2 = 168 + 4 Combine like terms: 168 + 4 = 172 4 + -4n + n2 = 172 Factor a perfect square on the left side: (n + -2)(n + -2) = 172 Calculate the square root of the right side: 13.114877049 Break this problem into two subproblems by setting (n + -2) equal to 13.114877049 and -13.114877049.Subproblem 1
n + -2 = 13.114877049 Simplifying n + -2 = 13.114877049 Reorder the terms: -2 + n = 13.114877049 Solving -2 + n = 13.114877049 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 13.114877049 + 2 Combine like terms: -2 + 2 = 0 0 + n = 13.114877049 + 2 n = 13.114877049 + 2 Combine like terms: 13.114877049 + 2 = 15.114877049 n = 15.114877049 Simplifying n = 15.114877049Subproblem 2
n + -2 = -13.114877049 Simplifying n + -2 = -13.114877049 Reorder the terms: -2 + n = -13.114877049 Solving -2 + n = -13.114877049 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -13.114877049 + 2 Combine like terms: -2 + 2 = 0 0 + n = -13.114877049 + 2 n = -13.114877049 + 2 Combine like terms: -13.114877049 + 2 = -11.114877049 n = -11.114877049 Simplifying n = -11.114877049Solution
The solution to the problem is based on the solutions from the subproblems. n = {15.114877049, -11.114877049}
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