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Simplifying n2 + -3n + -442 = 0 Reorder the terms: -442 + -3n + n2 = 0 Solving -442 + -3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '442' to each side of the equation. -442 + -3n + 442 + n2 = 0 + 442 Reorder the terms: -442 + 442 + -3n + n2 = 0 + 442 Combine like terms: -442 + 442 = 0 0 + -3n + n2 = 0 + 442 -3n + n2 = 0 + 442 Combine like terms: 0 + 442 = 442 -3n + n2 = 442 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 442 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 442 + 2.25 Combine like terms: 442 + 2.25 = 444.25 2.25 + -3n + n2 = 444.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 444.25 Calculate the square root of the right side: 21.077238908 Break this problem into two subproblems by setting (n + -1.5) equal to 21.077238908 and -21.077238908.Subproblem 1
n + -1.5 = 21.077238908 Simplifying n + -1.5 = 21.077238908 Reorder the terms: -1.5 + n = 21.077238908 Solving -1.5 + n = 21.077238908 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 21.077238908 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 21.077238908 + 1.5 n = 21.077238908 + 1.5 Combine like terms: 21.077238908 + 1.5 = 22.577238908 n = 22.577238908 Simplifying n = 22.577238908Subproblem 2
n + -1.5 = -21.077238908 Simplifying n + -1.5 = -21.077238908 Reorder the terms: -1.5 + n = -21.077238908 Solving -1.5 + n = -21.077238908 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -21.077238908 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -21.077238908 + 1.5 n = -21.077238908 + 1.5 Combine like terms: -21.077238908 + 1.5 = -19.577238908 n = -19.577238908 Simplifying n = -19.577238908Solution
The solution to the problem is based on the solutions from the subproblems. n = {22.577238908, -19.577238908}
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