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Simplifying n2 + 4n + -60 = 40 Reorder the terms: -60 + 4n + n2 = 40 Solving -60 + 4n + n2 = 40 Solving for variable 'n'. Reorder the terms: -60 + -40 + 4n + n2 = 40 + -40 Combine like terms: -60 + -40 = -100 -100 + 4n + n2 = 40 + -40 Combine like terms: 40 + -40 = 0 -100 + 4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 4n + 100 + n2 = 0 + 100 Reorder the terms: -100 + 100 + 4n + n2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 4n + n2 = 0 + 100 4n + n2 = 0 + 100 Combine like terms: 0 + 100 = 100 4n + n2 = 100 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 = 100 + 4 Reorder the terms: 4 + 4n + n2 = 100 + 4 Combine like terms: 100 + 4 = 104 4 + 4n + n2 = 104 Factor a perfect square on the left side: (n + 2)(n + 2) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (n + 2) equal to 10.198039027 and -10.198039027.Subproblem 1
n + 2 = 10.198039027 Simplifying n + 2 = 10.198039027 Reorder the terms: 2 + n = 10.198039027 Solving 2 + n = 10.198039027 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 = 10.198039027 + -2 Combine like terms: 2 + -2 = 0 0 + n = 10.198039027 + -2 n = 10.198039027 + -2 Combine like terms: 10.198039027 + -2 = 8.198039027 n = 8.198039027 Simplifying n = 8.198039027Subproblem 2
n + 2 = -10.198039027 Simplifying n + 2 = -10.198039027 Reorder the terms: 2 + n = -10.198039027 Solving 2 + n = -10.198039027 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 = -10.198039027 + -2 Combine like terms: 2 + -2 = 0 0 + n = -10.198039027 + -2 n = -10.198039027 + -2 Combine like terms: -10.198039027 + -2 = -12.198039027 n = -12.198039027 Simplifying n = -12.198039027Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.198039027, -12.198039027}
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