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Simplifying 5n2 + -87n + 322 = 7n + 2 Reorder the terms: 322 + -87n + 5n2 = 7n + 2 Reorder the terms: 322 + -87n + 5n2 = 2 + 7n Solving 322 + -87n + 5n2 = 2 + 7n Solving for variable 'n'. Reorder the terms: 322 + -2 + -87n + -7n + 5n2 = 2 + 7n + -2 + -7n Combine like terms: 322 + -2 = 320 320 + -87n + -7n + 5n2 = 2 + 7n + -2 + -7n Combine like terms: -87n + -7n = -94n 320 + -94n + 5n2 = 2 + 7n + -2 + -7n Reorder the terms: 320 + -94n + 5n2 = 2 + -2 + 7n + -7n Combine like terms: 2 + -2 = 0 320 + -94n + 5n2 = 0 + 7n + -7n 320 + -94n + 5n2 = 7n + -7n Combine like terms: 7n + -7n = 0 320 + -94n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 64 + -18.8n + n2 = 0 Move the constant term to the right: Add '-64' to each side of the equation. 64 + -18.8n + -64 + n2 = 0 + -64 Reorder the terms: 64 + -64 + -18.8n + n2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -18.8n + n2 = 0 + -64 -18.8n + n2 = 0 + -64 Combine like terms: 0 + -64 = -64 -18.8n + n2 = -64 The n term is -18.8n. Take half its coefficient (-9.4). Square it (88.36) and add it to both sides. Add '88.36' to each side of the equation. -18.8n + 88.36 + n2 = -64 + 88.36 Reorder the terms: 88.36 + -18.8n + n2 = -64 + 88.36 Combine like terms: -64 + 88.36 = 24.36 88.36 + -18.8n + n2 = 24.36 Factor a perfect square on the left side: (n + -9.4)(n + -9.4) = 24.36 Calculate the square root of the right side: 4.935585072 Break this problem into two subproblems by setting (n + -9.4) equal to 4.935585072 and -4.935585072.Subproblem 1
n + -9.4 = 4.935585072 Simplifying n + -9.4 = 4.935585072 Reorder the terms: -9.4 + n = 4.935585072 Solving -9.4 + n = 4.935585072 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '9.4' to each side of the equation. -9.4 + 9.4 + n = 4.935585072 + 9.4 Combine like terms: -9.4 + 9.4 = 0.0 0.0 + n = 4.935585072 + 9.4 n = 4.935585072 + 9.4 Combine like terms: 4.935585072 + 9.4 = 14.335585072 n = 14.335585072 Simplifying n = 14.335585072Subproblem 2
n + -9.4 = -4.935585072 Simplifying n + -9.4 = -4.935585072 Reorder the terms: -9.4 + n = -4.935585072 Solving -9.4 + n = -4.935585072 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '9.4' to each side of the equation. -9.4 + 9.4 + n = -4.935585072 + 9.4 Combine like terms: -9.4 + 9.4 = 0.0 0.0 + n = -4.935585072 + 9.4 n = -4.935585072 + 9.4 Combine like terms: -4.935585072 + 9.4 = 4.464414928 n = 4.464414928 Simplifying n = 4.464414928Solution
The solution to the problem is based on the solutions from the subproblems. n = {14.335585072, 4.464414928}
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