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Simplifying n2 + -8n = 8 Reorder the terms: -8n + n2 = 8 Solving -8n + n2 = 8 Solving for variable 'n'. Reorder the terms: -8 + -8n + n2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -8n + 8 + n2 = 0 + 8 Reorder the terms: -8 + 8 + -8n + n2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -8n + n2 = 0 + 8 -8n + n2 = 0 + 8 Combine like terms: 0 + 8 = 8 -8n + n2 = 8 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 = 8 + 16 Reorder the terms: 16 + -8n + n2 = 8 + 16 Combine like terms: 8 + 16 = 24 16 + -8n + n2 = 24 Factor a perfect square on the left side: (n + -4)(n + -4) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (n + -4) equal to 4.898979486 and -4.898979486.Subproblem 1
n + -4 = 4.898979486 Simplifying n + -4 = 4.898979486 Reorder the terms: -4 + n = 4.898979486 Solving -4 + n = 4.898979486 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 = 4.898979486 + 4 Combine like terms: -4 + 4 = 0 0 + n = 4.898979486 + 4 n = 4.898979486 + 4 Combine like terms: 4.898979486 + 4 = 8.898979486 n = 8.898979486 Simplifying n = 8.898979486Subproblem 2
n + -4 = -4.898979486 Simplifying n + -4 = -4.898979486 Reorder the terms: -4 + n = -4.898979486 Solving -4 + n = -4.898979486 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 = -4.898979486 + 4 Combine like terms: -4 + 4 = 0 0 + n = -4.898979486 + 4 n = -4.898979486 + 4 Combine like terms: -4.898979486 + 4 = -0.898979486 n = -0.898979486 Simplifying n = -0.898979486Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.898979486, -0.898979486}
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