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Simplifying n2 + -65n + -1400 = 0 Reorder the terms: -1400 + -65n + n2 = 0 Solving -1400 + -65n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '1400' to each side of the equation. -1400 + -65n + 1400 + n2 = 0 + 1400 Reorder the terms: -1400 + 1400 + -65n + n2 = 0 + 1400 Combine like terms: -1400 + 1400 = 0 0 + -65n + n2 = 0 + 1400 -65n + n2 = 0 + 1400 Combine like terms: 0 + 1400 = 1400 -65n + n2 = 1400 The n term is -65n. Take half its coefficient (-32.5). Square it (1056.25) and add it to both sides. Add '1056.25' to each side of the equation. -65n + 1056.25 + n2 = 1400 + 1056.25 Reorder the terms: 1056.25 + -65n + n2 = 1400 + 1056.25 Combine like terms: 1400 + 1056.25 = 2456.25 1056.25 + -65n + n2 = 2456.25 Factor a perfect square on the left side: (n + -32.5)(n + -32.5) = 2456.25 Calculate the square root of the right side: 49.560569004 Break this problem into two subproblems by setting (n + -32.5) equal to 49.560569004 and -49.560569004.Subproblem 1
n + -32.5 = 49.560569004 Simplifying n + -32.5 = 49.560569004 Reorder the terms: -32.5 + n = 49.560569004 Solving -32.5 + n = 49.560569004 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '32.5' to each side of the equation. -32.5 + 32.5 + n = 49.560569004 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + n = 49.560569004 + 32.5 n = 49.560569004 + 32.5 Combine like terms: 49.560569004 + 32.5 = 82.060569004 n = 82.060569004 Simplifying n = 82.060569004Subproblem 2
n + -32.5 = -49.560569004 Simplifying n + -32.5 = -49.560569004 Reorder the terms: -32.5 + n = -49.560569004 Solving -32.5 + n = -49.560569004 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '32.5' to each side of the equation. -32.5 + 32.5 + n = -49.560569004 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + n = -49.560569004 + 32.5 n = -49.560569004 + 32.5 Combine like terms: -49.560569004 + 32.5 = -17.060569004 n = -17.060569004 Simplifying n = -17.060569004Solution
The solution to the problem is based on the solutions from the subproblems. n = {82.060569004, -17.060569004}
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