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Simplifying 0 = n2 + 4n + -144 Reorder the terms: 0 = -144 + 4n + n2 Solving 0 = -144 + 4n + n2 Solving for variable 'n'. Combine like terms: 0 + 144 = 144 144 + -4n + -1n2 = -144 + 4n + n2 + 144 + -4n + -1n2 Reorder the terms: 144 + -4n + -1n2 = -144 + 144 + 4n + -4n + n2 + -1n2 Combine like terms: -144 + 144 = 0 144 + -4n + -1n2 = 0 + 4n + -4n + n2 + -1n2 144 + -4n + -1n2 = 4n + -4n + n2 + -1n2 Combine like terms: 4n + -4n = 0 144 + -4n + -1n2 = 0 + n2 + -1n2 144 + -4n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 144 + -4n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -144 + 4n + n2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + 4n + 144 + n2 = 0 + 144 Reorder the terms: -144 + 144 + 4n + n2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 4n + n2 = 0 + 144 4n + n2 = 0 + 144 Combine like terms: 0 + 144 = 144 4n + n2 = 144 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 = 144 + 4 Reorder the terms: 4 + 4n + n2 = 144 + 4 Combine like terms: 144 + 4 = 148 4 + 4n + n2 = 148 Factor a perfect square on the left side: (n + 2)(n + 2) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (n + 2) equal to 12.165525061 and -12.165525061.Subproblem 1
n + 2 = 12.165525061 Simplifying n + 2 = 12.165525061 Reorder the terms: 2 + n = 12.165525061 Solving 2 + n = 12.165525061 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 = 12.165525061 + -2 Combine like terms: 2 + -2 = 0 0 + n = 12.165525061 + -2 n = 12.165525061 + -2 Combine like terms: 12.165525061 + -2 = 10.165525061 n = 10.165525061 Simplifying n = 10.165525061Subproblem 2
n + 2 = -12.165525061 Simplifying n + 2 = -12.165525061 Reorder the terms: 2 + n = -12.165525061 Solving 2 + n = -12.165525061 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 = -12.165525061 + -2 Combine like terms: 2 + -2 = 0 0 + n = -12.165525061 + -2 n = -12.165525061 + -2 Combine like terms: -12.165525061 + -2 = -14.165525061 n = -14.165525061 Simplifying n = -14.165525061Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.165525061, -14.165525061}
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