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Simplifying n2 + 2n + -10.3 = 0 Reorder the terms: -10.3 + 2n + n2 = 0 Solving -10.3 + 2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '10.3' to each side of the equation. -10.3 + 2n + 10.3 + n2 = 0 + 10.3 Reorder the terms: -10.3 + 10.3 + 2n + n2 = 0 + 10.3 Combine like terms: -10.3 + 10.3 = 0.0 0.0 + 2n + n2 = 0 + 10.3 2n + n2 = 0 + 10.3 Combine like terms: 0 + 10.3 = 10.3 2n + n2 = 10.3 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 = 10.3 + 1 Reorder the terms: 1 + 2n + n2 = 10.3 + 1 Combine like terms: 10.3 + 1 = 11.3 1 + 2n + n2 = 11.3 Factor a perfect square on the left side: (n + 1)(n + 1) = 11.3 Calculate the square root of the right side: 3.361547263 Break this problem into two subproblems by setting (n + 1) equal to 3.361547263 and -3.361547263.Subproblem 1
n + 1 = 3.361547263 Simplifying n + 1 = 3.361547263 Reorder the terms: 1 + n = 3.361547263 Solving 1 + n = 3.361547263 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 = 3.361547263 + -1 Combine like terms: 1 + -1 = 0 0 + n = 3.361547263 + -1 n = 3.361547263 + -1 Combine like terms: 3.361547263 + -1 = 2.361547263 n = 2.361547263 Simplifying n = 2.361547263Subproblem 2
n + 1 = -3.361547263 Simplifying n + 1 = -3.361547263 Reorder the terms: 1 + n = -3.361547263 Solving 1 + n = -3.361547263 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 = -3.361547263 + -1 Combine like terms: 1 + -1 = 0 0 + n = -3.361547263 + -1 n = -3.361547263 + -1 Combine like terms: -3.361547263 + -1 = -4.361547263 n = -4.361547263 Simplifying n = -4.361547263Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.361547263, -4.361547263}
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