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Simplifying -8(n) = n2 + -3 Reorder the terms: -8n = -3 + n2 Solving -8n = -3 + n2 Solving for variable 'n'. Reorder the terms: 3 + -8n + -1n2 = -3 + n2 + 3 + -1n2 Reorder the terms: 3 + -8n + -1n2 = -3 + 3 + n2 + -1n2 Combine like terms: -3 + 3 = 0 3 + -8n + -1n2 = 0 + n2 + -1n2 3 + -8n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 3 + -8n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 8n + n2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 8n + 3 + n2 = 0 + 3 Reorder the terms: -3 + 3 + 8n + n2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 8n + n2 = 0 + 3 8n + n2 = 0 + 3 Combine like terms: 0 + 3 = 3 8n + n2 = 3 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 = 3 + 16 Reorder the terms: 16 + 8n + n2 = 3 + 16 Combine like terms: 3 + 16 = 19 16 + 8n + n2 = 19 Factor a perfect square on the left side: (n + 4)(n + 4) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (n + 4) equal to 4.358898944 and -4.358898944.Subproblem 1
n + 4 = 4.358898944 Simplifying n + 4 = 4.358898944 Reorder the terms: 4 + n = 4.358898944 Solving 4 + n = 4.358898944 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 = 4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + n = 4.358898944 + -4 n = 4.358898944 + -4 Combine like terms: 4.358898944 + -4 = 0.358898944 n = 0.358898944 Simplifying n = 0.358898944Subproblem 2
n + 4 = -4.358898944 Simplifying n + 4 = -4.358898944 Reorder the terms: 4 + n = -4.358898944 Solving 4 + n = -4.358898944 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 = -4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + n = -4.358898944 + -4 n = -4.358898944 + -4 Combine like terms: -4.358898944 + -4 = -8.358898944 n = -8.358898944 Simplifying n = -8.358898944Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.358898944, -8.358898944}
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