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Simplifying n2 + -9n + -4 = 0 Reorder the terms: -4 + -9n + n2 = 0 Solving -4 + -9n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -9n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + -9n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -9n + n2 = 0 + 4 -9n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 -9n + n2 = 4 The n term is -9n. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9n + 20.25 + n2 = 4 + 20.25 Reorder the terms: 20.25 + -9n + n2 = 4 + 20.25 Combine like terms: 4 + 20.25 = 24.25 20.25 + -9n + n2 = 24.25 Factor a perfect square on the left side: (n + -4.5)(n + -4.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (n + -4.5) equal to 4.924428901 and -4.924428901.Subproblem 1
n + -4.5 = 4.924428901 Simplifying n + -4.5 = 4.924428901 Reorder the terms: -4.5 + n = 4.924428901 Solving -4.5 + n = 4.924428901 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = 4.924428901 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = 4.924428901 + 4.5 n = 4.924428901 + 4.5 Combine like terms: 4.924428901 + 4.5 = 9.424428901 n = 9.424428901 Simplifying n = 9.424428901Subproblem 2
n + -4.5 = -4.924428901 Simplifying n + -4.5 = -4.924428901 Reorder the terms: -4.5 + n = -4.924428901 Solving -4.5 + n = -4.924428901 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = -4.924428901 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = -4.924428901 + 4.5 n = -4.924428901 + 4.5 Combine like terms: -4.924428901 + 4.5 = -0.424428901 n = -0.424428901 Simplifying n = -0.424428901Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.424428901, -0.424428901}
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