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Simplifying 4 = n(5n + -9) Reorder the terms: 4 = n(-9 + 5n) 4 = (-9 * n + 5n * n) 4 = (-9n + 5n2) Solving 4 = -9n + 5n2 Solving for variable 'n'. Reorder the terms: 4 + 9n + -5n2 = -9n + 9n + 5n2 + -5n2 Combine like terms: -9n + 9n = 0 4 + 9n + -5n2 = 0 + 5n2 + -5n2 4 + 9n + -5n2 = 5n2 + -5n2 Combine like terms: 5n2 + -5n2 = 0 4 + 9n + -5n2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.8 + -1.8n + n2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -1.8n + 0.8 + n2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -1.8n + n2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -1.8n + n2 = 0 + 0.8 -1.8n + n2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -1.8n + n2 = 0.8 The n term is -1.8n. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8n + 0.81 + n2 = 0.8 + 0.81 Reorder the terms: 0.81 + -1.8n + n2 = 0.8 + 0.81 Combine like terms: 0.8 + 0.81 = 1.61 0.81 + -1.8n + n2 = 1.61 Factor a perfect square on the left side: (n + -0.9)(n + -0.9) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (n + -0.9) equal to 1.268857754 and -1.268857754.Subproblem 1
n + -0.9 = 1.268857754 Simplifying n + -0.9 = 1.268857754 Reorder the terms: -0.9 + n = 1.268857754 Solving -0.9 + n = 1.268857754 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + n = 1.268857754 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + n = 1.268857754 + 0.9 n = 1.268857754 + 0.9 Combine like terms: 1.268857754 + 0.9 = 2.168857754 n = 2.168857754 Simplifying n = 2.168857754Subproblem 2
n + -0.9 = -1.268857754 Simplifying n + -0.9 = -1.268857754 Reorder the terms: -0.9 + n = -1.268857754 Solving -0.9 + n = -1.268857754 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + n = -1.268857754 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + n = -1.268857754 + 0.9 n = -1.268857754 + 0.9 Combine like terms: -1.268857754 + 0.9 = -0.368857754 n = -0.368857754 Simplifying n = -0.368857754Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.168857754, -0.368857754}
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