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Simplifying n = n * n + -7 Multiply n * n n = n2 + -7 Reorder the terms: n = -7 + n2 Solving n = -7 + n2 Solving for variable 'n'. Reorder the terms: 7 + n + -1n2 = -7 + n2 + 7 + -1n2 Reorder the terms: 7 + n + -1n2 = -7 + 7 + n2 + -1n2 Combine like terms: -7 + 7 = 0 7 + n + -1n2 = 0 + n2 + -1n2 7 + n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 7 + n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -1n + n2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -1n + 7 + n2 = 0 + 7 Reorder the terms: -7 + 7 + -1n + n2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1n + n2 = 0 + 7 -1n + n2 = 0 + 7 Combine like terms: 0 + 7 = 7 -1n + n2 = 7 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 7 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 7 + 0.25 Combine like terms: 7 + 0.25 = 7.25 0.25 + -1n + n2 = 7.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (n + 0.5) equal to 2.692582404 and -2.692582404.Subproblem 1
n + 0.5 = 2.692582404 Simplifying n + 0.5 = 2.692582404 Reorder the terms: 0.5 + n = 2.692582404 Solving 0.5 + n = 2.692582404 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 2.692582404 + -0.5 n = 2.692582404 + -0.5 Combine like terms: 2.692582404 + -0.5 = 2.192582404 n = 2.192582404 Simplifying n = 2.192582404Subproblem 2
n + 0.5 = -2.692582404 Simplifying n + 0.5 = -2.692582404 Reorder the terms: 0.5 + n = -2.692582404 Solving 0.5 + n = -2.692582404 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -2.692582404 + -0.5 n = -2.692582404 + -0.5 Combine like terms: -2.692582404 + -0.5 = -3.192582404 n = -3.192582404 Simplifying n = -3.192582404Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.192582404, -3.192582404}
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