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Simplifying n2 + -1n = 561 Reorder the terms: -1n + n2 = 561 Solving -1n + n2 = 561 Solving for variable 'n'. Reorder the terms: -561 + -1n + n2 = 561 + -561 Combine like terms: 561 + -561 = 0 -561 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '561' to each side of the equation. -561 + -1n + 561 + n2 = 0 + 561 Reorder the terms: -561 + 561 + -1n + n2 = 0 + 561 Combine like terms: -561 + 561 = 0 0 + -1n + n2 = 0 + 561 -1n + n2 = 0 + 561 Combine like terms: 0 + 561 = 561 -1n + n2 = 561 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 561 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 561 + 0.25 Combine like terms: 561 + 0.25 = 561.25 0.25 + -1n + n2 = 561.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 561.25 Calculate the square root of the right side: 23.690715481 Break this problem into two subproblems by setting (n + -0.5) equal to 23.690715481 and -23.690715481.Subproblem 1
n + -0.5 = 23.690715481 Simplifying n + -0.5 = 23.690715481 Reorder the terms: -0.5 + n = 23.690715481 Solving -0.5 + n = 23.690715481 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 23.690715481 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 23.690715481 + 0.5 n = 23.690715481 + 0.5 Combine like terms: 23.690715481 + 0.5 = 24.190715481 n = 24.190715481 Simplifying n = 24.190715481Subproblem 2
n + -0.5 = -23.690715481 Simplifying n + -0.5 = -23.690715481 Reorder the terms: -0.5 + n = -23.690715481 Solving -0.5 + n = -23.690715481 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -23.690715481 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -23.690715481 + 0.5 n = -23.690715481 + 0.5 Combine like terms: -23.690715481 + 0.5 = -23.190715481 n = -23.190715481 Simplifying n = -23.190715481Solution
The solution to the problem is based on the solutions from the subproblems. n = {24.190715481, -23.190715481}
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