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Simplifying n2 + -3n + -22 = 0 Reorder the terms: -22 + -3n + n2 = 0 Solving -22 + -3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -3n + 22 + n2 = 0 + 22 Reorder the terms: -22 + 22 + -3n + n2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -3n + n2 = 0 + 22 -3n + n2 = 0 + 22 Combine like terms: 0 + 22 = 22 -3n + n2 = 22 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 = 22 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 22 + 2.25 Combine like terms: 22 + 2.25 = 24.25 2.25 + -3n + n2 = 24.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (n + -1.5) equal to 4.924428901 and -4.924428901.Subproblem 1
n + -1.5 = 4.924428901 Simplifying n + -1.5 = 4.924428901 Reorder the terms: -1.5 + n = 4.924428901 Solving -1.5 + n = 4.924428901 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 = 4.924428901 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 4.924428901 + 1.5 n = 4.924428901 + 1.5 Combine like terms: 4.924428901 + 1.5 = 6.424428901 n = 6.424428901 Simplifying n = 6.424428901Subproblem 2
n + -1.5 = -4.924428901 Simplifying n + -1.5 = -4.924428901 Reorder the terms: -1.5 + n = -4.924428901 Solving -1.5 + n = -4.924428901 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 = -4.924428901 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -4.924428901 + 1.5 n = -4.924428901 + 1.5 Combine like terms: -4.924428901 + 1.5 = -3.424428901 n = -3.424428901 Simplifying n = -3.424428901Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.424428901, -3.424428901}
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