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Simplifying 8n2 + -14n + -148 = -4 + n + 7n2 Reorder the terms: -148 + -14n + 8n2 = -4 + n + 7n2 Solving -148 + -14n + 8n2 = -4 + n + 7n2 Solving for variable 'n'. Reorder the terms: -148 + 4 + -14n + -1n + 8n2 + -7n2 = -4 + n + 7n2 + 4 + -1n + -7n2 Combine like terms: -148 + 4 = -144 -144 + -14n + -1n + 8n2 + -7n2 = -4 + n + 7n2 + 4 + -1n + -7n2 Combine like terms: -14n + -1n = -15n -144 + -15n + 8n2 + -7n2 = -4 + n + 7n2 + 4 + -1n + -7n2 Combine like terms: 8n2 + -7n2 = 1n2 -144 + -15n + 1n2 = -4 + n + 7n2 + 4 + -1n + -7n2 Reorder the terms: -144 + -15n + 1n2 = -4 + 4 + n + -1n + 7n2 + -7n2 Combine like terms: -4 + 4 = 0 -144 + -15n + 1n2 = 0 + n + -1n + 7n2 + -7n2 -144 + -15n + 1n2 = n + -1n + 7n2 + -7n2 Combine like terms: n + -1n = 0 -144 + -15n + 1n2 = 0 + 7n2 + -7n2 -144 + -15n + 1n2 = 7n2 + -7n2 Combine like terms: 7n2 + -7n2 = 0 -144 + -15n + 1n2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -15n + 144 + n2 = 0 + 144 Reorder the terms: -144 + 144 + -15n + n2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -15n + n2 = 0 + 144 -15n + n2 = 0 + 144 Combine like terms: 0 + 144 = 144 -15n + n2 = 144 The n term is -15n. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15n + 56.25 + n2 = 144 + 56.25 Reorder the terms: 56.25 + -15n + n2 = 144 + 56.25 Combine like terms: 144 + 56.25 = 200.25 56.25 + -15n + n2 = 200.25 Factor a perfect square on the left side: (n + -7.5)(n + -7.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (n + -7.5) equal to 14.150971698 and -14.150971698.Subproblem 1
n + -7.5 = 14.150971698 Simplifying n + -7.5 = 14.150971698 Reorder the terms: -7.5 + n = 14.150971698 Solving -7.5 + n = 14.150971698 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + n = 14.150971698 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + n = 14.150971698 + 7.5 n = 14.150971698 + 7.5 Combine like terms: 14.150971698 + 7.5 = 21.650971698 n = 21.650971698 Simplifying n = 21.650971698Subproblem 2
n + -7.5 = -14.150971698 Simplifying n + -7.5 = -14.150971698 Reorder the terms: -7.5 + n = -14.150971698 Solving -7.5 + n = -14.150971698 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + n = -14.150971698 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + n = -14.150971698 + 7.5 n = -14.150971698 + 7.5 Combine like terms: -14.150971698 + 7.5 = -6.650971698 n = -6.650971698 Simplifying n = -6.650971698Solution
The solution to the problem is based on the solutions from the subproblems. n = {21.650971698, -6.650971698}
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