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Simplifying n2 + -1n = 644 Reorder the terms: -1n + n2 = 644 Solving -1n + n2 = 644 Solving for variable 'n'. Reorder the terms: -644 + -1n + n2 = 644 + -644 Combine like terms: 644 + -644 = 0 -644 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '644' to each side of the equation. -644 + -1n + 644 + n2 = 0 + 644 Reorder the terms: -644 + 644 + -1n + n2 = 0 + 644 Combine like terms: -644 + 644 = 0 0 + -1n + n2 = 0 + 644 -1n + n2 = 0 + 644 Combine like terms: 0 + 644 = 644 -1n + n2 = 644 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 = 644 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 644 + 0.25 Combine like terms: 644 + 0.25 = 644.25 0.25 + -1n + n2 = 644.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 644.25 Calculate the square root of the right side: 25.382080293 Break this problem into two subproblems by setting (n + -0.5) equal to 25.382080293 and -25.382080293.Subproblem 1
n + -0.5 = 25.382080293 Simplifying n + -0.5 = 25.382080293 Reorder the terms: -0.5 + n = 25.382080293 Solving -0.5 + n = 25.382080293 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 = 25.382080293 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 25.382080293 + 0.5 n = 25.382080293 + 0.5 Combine like terms: 25.382080293 + 0.5 = 25.882080293 n = 25.882080293 Simplifying n = 25.882080293Subproblem 2
n + -0.5 = -25.382080293 Simplifying n + -0.5 = -25.382080293 Reorder the terms: -0.5 + n = -25.382080293 Solving -0.5 + n = -25.382080293 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 = -25.382080293 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -25.382080293 + 0.5 n = -25.382080293 + 0.5 Combine like terms: -25.382080293 + 0.5 = -24.882080293 n = -24.882080293 Simplifying n = -24.882080293Solution
The solution to the problem is based on the solutions from the subproblems. n = {25.882080293, -24.882080293}
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