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Simplifying n2 + n + -576 = 0 Reorder the terms: -576 + n + n2 = 0 Solving -576 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '576' to each side of the equation. -576 + n + 576 + n2 = 0 + 576 Reorder the terms: -576 + 576 + n + n2 = 0 + 576 Combine like terms: -576 + 576 = 0 0 + n + n2 = 0 + 576 n + n2 = 0 + 576 Combine like terms: 0 + 576 = 576 n + n2 = 576 The n term is n. 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. n + 0.25 + n2 = 576 + 0.25 Reorder the terms: 0.25 + n + n2 = 576 + 0.25 Combine like terms: 576 + 0.25 = 576.25 0.25 + n + n2 = 576.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 576.25 Calculate the square root of the right side: 24.005207768 Break this problem into two subproblems by setting (n + 0.5) equal to 24.005207768 and -24.005207768.Subproblem 1
n + 0.5 = 24.005207768 Simplifying n + 0.5 = 24.005207768 Reorder the terms: 0.5 + n = 24.005207768 Solving 0.5 + n = 24.005207768 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 = 24.005207768 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 24.005207768 + -0.5 n = 24.005207768 + -0.5 Combine like terms: 24.005207768 + -0.5 = 23.505207768 n = 23.505207768 Simplifying n = 23.505207768Subproblem 2
n + 0.5 = -24.005207768 Simplifying n + 0.5 = -24.005207768 Reorder the terms: 0.5 + n = -24.005207768 Solving 0.5 + n = -24.005207768 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 = -24.005207768 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -24.005207768 + -0.5 n = -24.005207768 + -0.5 Combine like terms: -24.005207768 + -0.5 = -24.505207768 n = -24.505207768 Simplifying n = -24.505207768Solution
The solution to the problem is based on the solutions from the subproblems. n = {23.505207768, -24.505207768}
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