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Simplifying n2 + 21n + -60 = 0 Reorder the terms: -60 + 21n + n2 = 0 Solving -60 + 21n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 21n + 60 + n2 = 0 + 60 Reorder the terms: -60 + 60 + 21n + n2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 21n + n2 = 0 + 60 21n + n2 = 0 + 60 Combine like terms: 0 + 60 = 60 21n + n2 = 60 The n term is 21n. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21n + 110.25 + n2 = 60 + 110.25 Reorder the terms: 110.25 + 21n + n2 = 60 + 110.25 Combine like terms: 60 + 110.25 = 170.25 110.25 + 21n + n2 = 170.25 Factor a perfect square on the left side: (n + 10.5)(n + 10.5) = 170.25 Calculate the square root of the right side: 13.047988351 Break this problem into two subproblems by setting (n + 10.5) equal to 13.047988351 and -13.047988351.Subproblem 1
n + 10.5 = 13.047988351 Simplifying n + 10.5 = 13.047988351 Reorder the terms: 10.5 + n = 13.047988351 Solving 10.5 + n = 13.047988351 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + n = 13.047988351 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + n = 13.047988351 + -10.5 n = 13.047988351 + -10.5 Combine like terms: 13.047988351 + -10.5 = 2.547988351 n = 2.547988351 Simplifying n = 2.547988351Subproblem 2
n + 10.5 = -13.047988351 Simplifying n + 10.5 = -13.047988351 Reorder the terms: 10.5 + n = -13.047988351 Solving 10.5 + n = -13.047988351 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + n = -13.047988351 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + n = -13.047988351 + -10.5 n = -13.047988351 + -10.5 Combine like terms: -13.047988351 + -10.5 = -23.547988351 n = -23.547988351 Simplifying n = -23.547988351Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.547988351, -23.547988351}
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