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Simplifying -1n2 + 8n + 48 = 42 Reorder the terms: 48 + 8n + -1n2 = 42 Solving 48 + 8n + -1n2 = 42 Solving for variable 'n'. Reorder the terms: 48 + -42 + 8n + -1n2 = 42 + -42 Combine like terms: 48 + -42 = 6 6 + 8n + -1n2 = 42 + -42 Combine like terms: 42 + -42 = 0 6 + 8n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + -8n + n2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -8n + 6 + n2 = 0 + 6 Reorder the terms: -6 + 6 + -8n + n2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -8n + n2 = 0 + 6 -8n + n2 = 0 + 6 Combine like terms: 0 + 6 = 6 -8n + n2 = 6 The n term is -8n. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8n + 16 + n2 = 6 + 16 Reorder the terms: 16 + -8n + n2 = 6 + 16 Combine like terms: 6 + 16 = 22 16 + -8n + n2 = 22 Factor a perfect square on the left side: (n + -4)(n + -4) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (n + -4) equal to 4.69041576 and -4.69041576.Subproblem 1
n + -4 = 4.69041576 Simplifying n + -4 = 4.69041576 Reorder the terms: -4 + n = 4.69041576 Solving -4 + n = 4.69041576 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n = 4.69041576 + 4 Combine like terms: -4 + 4 = 0 0 + n = 4.69041576 + 4 n = 4.69041576 + 4 Combine like terms: 4.69041576 + 4 = 8.69041576 n = 8.69041576 Simplifying n = 8.69041576Subproblem 2
n + -4 = -4.69041576 Simplifying n + -4 = -4.69041576 Reorder the terms: -4 + n = -4.69041576 Solving -4 + n = -4.69041576 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n = -4.69041576 + 4 Combine like terms: -4 + 4 = 0 0 + n = -4.69041576 + 4 n = -4.69041576 + 4 Combine like terms: -4.69041576 + 4 = -0.69041576 n = -0.69041576 Simplifying n = -0.69041576Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.69041576, -0.69041576}
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