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Simplifying 13n2 = 12n2 + 40n + 200 Reorder the terms: 13n2 = 200 + 40n + 12n2 Solving 13n2 = 200 + 40n + 12n2 Solving for variable 'n'. Reorder the terms: -200 + -40n + 13n2 + -12n2 = 200 + 40n + 12n2 + -200 + -40n + -12n2 Combine like terms: 13n2 + -12n2 = 1n2 -200 + -40n + 1n2 = 200 + 40n + 12n2 + -200 + -40n + -12n2 Reorder the terms: -200 + -40n + 1n2 = 200 + -200 + 40n + -40n + 12n2 + -12n2 Combine like terms: 200 + -200 = 0 -200 + -40n + 1n2 = 0 + 40n + -40n + 12n2 + -12n2 -200 + -40n + 1n2 = 40n + -40n + 12n2 + -12n2 Combine like terms: 40n + -40n = 0 -200 + -40n + 1n2 = 0 + 12n2 + -12n2 -200 + -40n + 1n2 = 12n2 + -12n2 Combine like terms: 12n2 + -12n2 = 0 -200 + -40n + 1n2 = 0 Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + -40n + 200 + n2 = 0 + 200 Reorder the terms: -200 + 200 + -40n + n2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -40n + n2 = 0 + 200 -40n + n2 = 0 + 200 Combine like terms: 0 + 200 = 200 -40n + n2 = 200 The n term is -40n. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40n + 400 + n2 = 200 + 400 Reorder the terms: 400 + -40n + n2 = 200 + 400 Combine like terms: 200 + 400 = 600 400 + -40n + n2 = 600 Factor a perfect square on the left side: (n + -20)(n + -20) = 600 Calculate the square root of the right side: 24.494897428 Break this problem into two subproblems by setting (n + -20) equal to 24.494897428 and -24.494897428.Subproblem 1
n + -20 = 24.494897428 Simplifying n + -20 = 24.494897428 Reorder the terms: -20 + n = 24.494897428 Solving -20 + n = 24.494897428 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + n = 24.494897428 + 20 Combine like terms: -20 + 20 = 0 0 + n = 24.494897428 + 20 n = 24.494897428 + 20 Combine like terms: 24.494897428 + 20 = 44.494897428 n = 44.494897428 Simplifying n = 44.494897428Subproblem 2
n + -20 = -24.494897428 Simplifying n + -20 = -24.494897428 Reorder the terms: -20 + n = -24.494897428 Solving -20 + n = -24.494897428 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + n = -24.494897428 + 20 Combine like terms: -20 + 20 = 0 0 + n = -24.494897428 + 20 n = -24.494897428 + 20 Combine like terms: -24.494897428 + 20 = -4.494897428 n = -4.494897428 Simplifying n = -4.494897428Solution
The solution to the problem is based on the solutions from the subproblems. n = {44.494897428, -4.494897428}
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