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Simplifying n2 + 2n + 5 = 1542 Reorder the terms: 5 + 2n + n2 = 1542 Solving 5 + 2n + n2 = 1542 Solving for variable 'n'. Reorder the terms: 5 + -1542 + 2n + n2 = 1542 + -1542 Combine like terms: 5 + -1542 = -1537 -1537 + 2n + n2 = 1542 + -1542 Combine like terms: 1542 + -1542 = 0 -1537 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '1537' to each side of the equation. -1537 + 2n + 1537 + n2 = 0 + 1537 Reorder the terms: -1537 + 1537 + 2n + n2 = 0 + 1537 Combine like terms: -1537 + 1537 = 0 0 + 2n + n2 = 0 + 1537 2n + n2 = 0 + 1537 Combine like terms: 0 + 1537 = 1537 2n + n2 = 1537 The n term is 2n. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2n + 1 + n2 = 1537 + 1 Reorder the terms: 1 + 2n + n2 = 1537 + 1 Combine like terms: 1537 + 1 = 1538 1 + 2n + n2 = 1538 Factor a perfect square on the left side: (n + 1)(n + 1) = 1538 Calculate the square root of the right side: 39.217343102 Break this problem into two subproblems by setting (n + 1) equal to 39.217343102 and -39.217343102.Subproblem 1
n + 1 = 39.217343102 Simplifying n + 1 = 39.217343102 Reorder the terms: 1 + n = 39.217343102 Solving 1 + n = 39.217343102 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 39.217343102 + -1 Combine like terms: 1 + -1 = 0 0 + n = 39.217343102 + -1 n = 39.217343102 + -1 Combine like terms: 39.217343102 + -1 = 38.217343102 n = 38.217343102 Simplifying n = 38.217343102Subproblem 2
n + 1 = -39.217343102 Simplifying n + 1 = -39.217343102 Reorder the terms: 1 + n = -39.217343102 Solving 1 + n = -39.217343102 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = -39.217343102 + -1 Combine like terms: 1 + -1 = 0 0 + n = -39.217343102 + -1 n = -39.217343102 + -1 Combine like terms: -39.217343102 + -1 = -40.217343102 n = -40.217343102 Simplifying n = -40.217343102Solution
The solution to the problem is based on the solutions from the subproblems. n = {38.217343102, -40.217343102}
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