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Simplifying (n + -8)(n + 1) = 35 Reorder the terms: (-8 + n)(n + 1) = 35 Reorder the terms: (-8 + n)(1 + n) = 35 Multiply (-8 + n) * (1 + n) (-8(1 + n) + n(1 + n)) = 35 ((1 * -8 + n * -8) + n(1 + n)) = 35 ((-8 + -8n) + n(1 + n)) = 35 (-8 + -8n + (1 * n + n * n)) = 35 (-8 + -8n + (1n + n2)) = 35 Combine like terms: -8n + 1n = -7n (-8 + -7n + n2) = 35 Solving -8 + -7n + n2 = 35 Solving for variable 'n'. Reorder the terms: -8 + -35 + -7n + n2 = 35 + -35 Combine like terms: -8 + -35 = -43 -43 + -7n + n2 = 35 + -35 Combine like terms: 35 + -35 = 0 -43 + -7n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -7n + 43 + n2 = 0 + 43 Reorder the terms: -43 + 43 + -7n + n2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -7n + n2 = 0 + 43 -7n + n2 = 0 + 43 Combine like terms: 0 + 43 = 43 -7n + n2 = 43 The n term is -7n. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7n + 12.25 + n2 = 43 + 12.25 Reorder the terms: 12.25 + -7n + n2 = 43 + 12.25 Combine like terms: 43 + 12.25 = 55.25 12.25 + -7n + n2 = 55.25 Factor a perfect square on the left side: (n + -3.5)(n + -3.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (n + -3.5) equal to 7.433034374 and -7.433034374.Subproblem 1
n + -3.5 = 7.433034374 Simplifying n + -3.5 = 7.433034374 Reorder the terms: -3.5 + n = 7.433034374 Solving -3.5 + n = 7.433034374 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + n = 7.433034374 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + n = 7.433034374 + 3.5 n = 7.433034374 + 3.5 Combine like terms: 7.433034374 + 3.5 = 10.933034374 n = 10.933034374 Simplifying n = 10.933034374Subproblem 2
n + -3.5 = -7.433034374 Simplifying n + -3.5 = -7.433034374 Reorder the terms: -3.5 + n = -7.433034374 Solving -3.5 + n = -7.433034374 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + n = -7.433034374 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + n = -7.433034374 + 3.5 n = -7.433034374 + 3.5 Combine like terms: -7.433034374 + 3.5 = -3.933034374 n = -3.933034374 Simplifying n = -3.933034374Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.933034374, -3.933034374}
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