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Simplifying n2 + 2n + -760 = 0 Reorder the terms: -760 + 2n + n2 = 0 Solving -760 + 2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '760' to each side of the equation. -760 + 2n + 760 + n2 = 0 + 760 Reorder the terms: -760 + 760 + 2n + n2 = 0 + 760 Combine like terms: -760 + 760 = 0 0 + 2n + n2 = 0 + 760 2n + n2 = 0 + 760 Combine like terms: 0 + 760 = 760 2n + n2 = 760 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 = 760 + 1 Reorder the terms: 1 + 2n + n2 = 760 + 1 Combine like terms: 760 + 1 = 761 1 + 2n + n2 = 761 Factor a perfect square on the left side: (n + 1)(n + 1) = 761 Calculate the square root of the right side: 27.586228448 Break this problem into two subproblems by setting (n + 1) equal to 27.586228448 and -27.586228448.Subproblem 1
n + 1 = 27.586228448 Simplifying n + 1 = 27.586228448 Reorder the terms: 1 + n = 27.586228448 Solving 1 + n = 27.586228448 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 = 27.586228448 + -1 Combine like terms: 1 + -1 = 0 0 + n = 27.586228448 + -1 n = 27.586228448 + -1 Combine like terms: 27.586228448 + -1 = 26.586228448 n = 26.586228448 Simplifying n = 26.586228448Subproblem 2
n + 1 = -27.586228448 Simplifying n + 1 = -27.586228448 Reorder the terms: 1 + n = -27.586228448 Solving 1 + n = -27.586228448 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 = -27.586228448 + -1 Combine like terms: 1 + -1 = 0 0 + n = -27.586228448 + -1 n = -27.586228448 + -1 Combine like terms: -27.586228448 + -1 = -28.586228448 n = -28.586228448 Simplifying n = -28.586228448Solution
The solution to the problem is based on the solutions from the subproblems. n = {26.586228448, -28.586228448}
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