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Simplifying n2 + 9n + -3 = 0 Reorder the terms: -3 + 9n + n2 = 0 Solving -3 + 9n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 9n + 3 + n2 = 0 + 3 Reorder the terms: -3 + 3 + 9n + n2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 9n + n2 = 0 + 3 9n + n2 = 0 + 3 Combine like terms: 0 + 3 = 3 9n + n2 = 3 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 = 3 + 20.25 Reorder the terms: 20.25 + 9n + n2 = 3 + 20.25 Combine like terms: 3 + 20.25 = 23.25 20.25 + 9n + n2 = 23.25 Factor a perfect square on the left side: (n + 4.5)(n + 4.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (n + 4.5) equal to 4.82182538 and -4.82182538.Subproblem 1
n + 4.5 = 4.82182538 Simplifying n + 4.5 = 4.82182538 Reorder the terms: 4.5 + n = 4.82182538 Solving 4.5 + n = 4.82182538 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 = 4.82182538 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + n = 4.82182538 + -4.5 n = 4.82182538 + -4.5 Combine like terms: 4.82182538 + -4.5 = 0.32182538 n = 0.32182538 Simplifying n = 0.32182538Subproblem 2
n + 4.5 = -4.82182538 Simplifying n + 4.5 = -4.82182538 Reorder the terms: 4.5 + n = -4.82182538 Solving 4.5 + n = -4.82182538 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 = -4.82182538 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + n = -4.82182538 + -4.5 n = -4.82182538 + -4.5 Combine like terms: -4.82182538 + -4.5 = -9.32182538 n = -9.32182538 Simplifying n = -9.32182538Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.32182538, -9.32182538}
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