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Simplifying 0 = 5n2 + -39n + -42 Reorder the terms: 0 = -42 + -39n + 5n2 Solving 0 = -42 + -39n + 5n2 Solving for variable 'n'. Combine like terms: 0 + 42 = 42 42 + 39n + -5n2 = -42 + -39n + 5n2 + 42 + 39n + -5n2 Reorder the terms: 42 + 39n + -5n2 = -42 + 42 + -39n + 39n + 5n2 + -5n2 Combine like terms: -42 + 42 = 0 42 + 39n + -5n2 = 0 + -39n + 39n + 5n2 + -5n2 42 + 39n + -5n2 = -39n + 39n + 5n2 + -5n2 Combine like terms: -39n + 39n = 0 42 + 39n + -5n2 = 0 + 5n2 + -5n2 42 + 39n + -5n2 = 5n2 + -5n2 Combine like terms: 5n2 + -5n2 = 0 42 + 39n + -5n2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -8.4 + -7.8n + n2 = 0 Move the constant term to the right: Add '8.4' to each side of the equation. -8.4 + -7.8n + 8.4 + n2 = 0 + 8.4 Reorder the terms: -8.4 + 8.4 + -7.8n + n2 = 0 + 8.4 Combine like terms: -8.4 + 8.4 = 0.0 0.0 + -7.8n + n2 = 0 + 8.4 -7.8n + n2 = 0 + 8.4 Combine like terms: 0 + 8.4 = 8.4 -7.8n + n2 = 8.4 The n term is -7.8n. Take half its coefficient (-3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. -7.8n + 15.21 + n2 = 8.4 + 15.21 Reorder the terms: 15.21 + -7.8n + n2 = 8.4 + 15.21 Combine like terms: 8.4 + 15.21 = 23.61 15.21 + -7.8n + n2 = 23.61 Factor a perfect square on the left side: (n + -3.9)(n + -3.9) = 23.61 Calculate the square root of the right side: 4.859012245 Break this problem into two subproblems by setting (n + -3.9) equal to 4.859012245 and -4.859012245.Subproblem 1
n + -3.9 = 4.859012245 Simplifying n + -3.9 = 4.859012245 Reorder the terms: -3.9 + n = 4.859012245 Solving -3.9 + n = 4.859012245 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + n = 4.859012245 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + n = 4.859012245 + 3.9 n = 4.859012245 + 3.9 Combine like terms: 4.859012245 + 3.9 = 8.759012245 n = 8.759012245 Simplifying n = 8.759012245Subproblem 2
n + -3.9 = -4.859012245 Simplifying n + -3.9 = -4.859012245 Reorder the terms: -3.9 + n = -4.859012245 Solving -3.9 + n = -4.859012245 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + n = -4.859012245 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + n = -4.859012245 + 3.9 n = -4.859012245 + 3.9 Combine like terms: -4.859012245 + 3.9 = -0.959012245 n = -0.959012245 Simplifying n = -0.959012245Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.759012245, -0.959012245}
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