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Simplifying 0 = n2 + 4n + -80 Reorder the terms: 0 = -80 + 4n + n2 Solving 0 = -80 + 4n + n2 Solving for variable 'n'. Combine like terms: 0 + 80 = 80 80 + -4n + -1n2 = -80 + 4n + n2 + 80 + -4n + -1n2 Reorder the terms: 80 + -4n + -1n2 = -80 + 80 + 4n + -4n + n2 + -1n2 Combine like terms: -80 + 80 = 0 80 + -4n + -1n2 = 0 + 4n + -4n + n2 + -1n2 80 + -4n + -1n2 = 4n + -4n + n2 + -1n2 Combine like terms: 4n + -4n = 0 80 + -4n + -1n2 = 0 + n2 + -1n2 80 + -4n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 80 + -4n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -80 + 4n + n2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 4n + 80 + n2 = 0 + 80 Reorder the terms: -80 + 80 + 4n + n2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 4n + n2 = 0 + 80 4n + n2 = 0 + 80 Combine like terms: 0 + 80 = 80 4n + n2 = 80 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 = 80 + 4 Reorder the terms: 4 + 4n + n2 = 80 + 4 Combine like terms: 80 + 4 = 84 4 + 4n + n2 = 84 Factor a perfect square on the left side: (n + 2)(n + 2) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (n + 2) equal to 9.16515139 and -9.16515139.Subproblem 1
n + 2 = 9.16515139 Simplifying n + 2 = 9.16515139 Reorder the terms: 2 + n = 9.16515139 Solving 2 + n = 9.16515139 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 = 9.16515139 + -2 Combine like terms: 2 + -2 = 0 0 + n = 9.16515139 + -2 n = 9.16515139 + -2 Combine like terms: 9.16515139 + -2 = 7.16515139 n = 7.16515139 Simplifying n = 7.16515139Subproblem 2
n + 2 = -9.16515139 Simplifying n + 2 = -9.16515139 Reorder the terms: 2 + n = -9.16515139 Solving 2 + n = -9.16515139 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 = -9.16515139 + -2 Combine like terms: 2 + -2 = 0 0 + n = -9.16515139 + -2 n = -9.16515139 + -2 Combine like terms: -9.16515139 + -2 = -11.16515139 n = -11.16515139 Simplifying n = -11.16515139Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.16515139, -11.16515139}
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