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Simplifying n2 + -160n + 340 = 0 Reorder the terms: 340 + -160n + n2 = 0 Solving 340 + -160n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-340' to each side of the equation. 340 + -160n + -340 + n2 = 0 + -340 Reorder the terms: 340 + -340 + -160n + n2 = 0 + -340 Combine like terms: 340 + -340 = 0 0 + -160n + n2 = 0 + -340 -160n + n2 = 0 + -340 Combine like terms: 0 + -340 = -340 -160n + n2 = -340 The n term is -160n. Take half its coefficient (-80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. -160n + 6400 + n2 = -340 + 6400 Reorder the terms: 6400 + -160n + n2 = -340 + 6400 Combine like terms: -340 + 6400 = 6060 6400 + -160n + n2 = 6060 Factor a perfect square on the left side: (n + -80)(n + -80) = 6060 Calculate the square root of the right side: 77.846001824 Break this problem into two subproblems by setting (n + -80) equal to 77.846001824 and -77.846001824.Subproblem 1
n + -80 = 77.846001824 Simplifying n + -80 = 77.846001824 Reorder the terms: -80 + n = 77.846001824 Solving -80 + n = 77.846001824 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + n = 77.846001824 + 80 Combine like terms: -80 + 80 = 0 0 + n = 77.846001824 + 80 n = 77.846001824 + 80 Combine like terms: 77.846001824 + 80 = 157.846001824 n = 157.846001824 Simplifying n = 157.846001824Subproblem 2
n + -80 = -77.846001824 Simplifying n + -80 = -77.846001824 Reorder the terms: -80 + n = -77.846001824 Solving -80 + n = -77.846001824 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + n = -77.846001824 + 80 Combine like terms: -80 + 80 = 0 0 + n = -77.846001824 + 80 n = -77.846001824 + 80 Combine like terms: -77.846001824 + 80 = 2.153998176 n = 2.153998176 Simplifying n = 2.153998176Solution
The solution to the problem is based on the solutions from the subproblems. n = {157.846001824, 2.153998176}
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