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Simplifying n2 + 5n = 12 Reorder the terms: 5n + n2 = 12 Solving 5n + n2 = 12 Solving for variable 'n'. Reorder the terms: -12 + 5n + n2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 5n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 5n + 12 + n2 = 0 + 12 Reorder the terms: -12 + 12 + 5n + n2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 5n + n2 = 0 + 12 5n + n2 = 0 + 12 Combine like terms: 0 + 12 = 12 5n + n2 = 12 The n term is 5n. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5n + 6.25 + n2 = 12 + 6.25 Reorder the terms: 6.25 + 5n + n2 = 12 + 6.25 Combine like terms: 12 + 6.25 = 18.25 6.25 + 5n + n2 = 18.25 Factor a perfect square on the left side: (n + 2.5)(n + 2.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (n + 2.5) equal to 4.272001873 and -4.272001873.Subproblem 1
n + 2.5 = 4.272001873 Simplifying n + 2.5 = 4.272001873 Reorder the terms: 2.5 + n = 4.272001873 Solving 2.5 + n = 4.272001873 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = 4.272001873 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = 4.272001873 + -2.5 n = 4.272001873 + -2.5 Combine like terms: 4.272001873 + -2.5 = 1.772001873 n = 1.772001873 Simplifying n = 1.772001873Subproblem 2
n + 2.5 = -4.272001873 Simplifying n + 2.5 = -4.272001873 Reorder the terms: 2.5 + n = -4.272001873 Solving 2.5 + n = -4.272001873 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = -4.272001873 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = -4.272001873 + -2.5 n = -4.272001873 + -2.5 Combine like terms: -4.272001873 + -2.5 = -6.772001873 n = -6.772001873 Simplifying n = -6.772001873Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.772001873, -6.772001873}
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