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Simplifying (n + -2) * 188n = 7 Reorder the terms: (-2 + n) * 188n = 7 Reorder the terms for easier multiplication: 188n(-2 + n) = 7 (-2 * 188n + n * 188n) = 7 (-376n + 188n2) = 7 Solving -376n + 188n2 = 7 Solving for variable 'n'. Reorder the terms: -7 + -376n + 188n2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -376n + 188n2 = 0 Begin completing the square. Divide all terms by 188 the coefficient of the squared term: Divide each side by '188'. -0.03723404255 + -2n + n2 = 0 Move the constant term to the right: Add '0.03723404255' to each side of the equation. -0.03723404255 + -2n + 0.03723404255 + n2 = 0 + 0.03723404255 Reorder the terms: -0.03723404255 + 0.03723404255 + -2n + n2 = 0 + 0.03723404255 Combine like terms: -0.03723404255 + 0.03723404255 = 0.00000000000 0.00000000000 + -2n + n2 = 0 + 0.03723404255 -2n + n2 = 0 + 0.03723404255 Combine like terms: 0 + 0.03723404255 = 0.03723404255 -2n + n2 = 0.03723404255 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 0.03723404255 + 1 Reorder the terms: 1 + -2n + n2 = 0.03723404255 + 1 Combine like terms: 0.03723404255 + 1 = 1.03723404255 1 + -2n + n2 = 1.03723404255 Factor a perfect square on the left side: (n + -1)(n + -1) = 1.03723404255 Calculate the square root of the right side: 1.018446878 Break this problem into two subproblems by setting (n + -1) equal to 1.018446878 and -1.018446878.Subproblem 1
n + -1 = 1.018446878 Simplifying n + -1 = 1.018446878 Reorder the terms: -1 + n = 1.018446878 Solving -1 + n = 1.018446878 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 1.018446878 + 1 Combine like terms: -1 + 1 = 0 0 + n = 1.018446878 + 1 n = 1.018446878 + 1 Combine like terms: 1.018446878 + 1 = 2.018446878 n = 2.018446878 Simplifying n = 2.018446878Subproblem 2
n + -1 = -1.018446878 Simplifying n + -1 = -1.018446878 Reorder the terms: -1 + n = -1.018446878 Solving -1 + n = -1.018446878 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -1.018446878 + 1 Combine like terms: -1 + 1 = 0 0 + n = -1.018446878 + 1 n = -1.018446878 + 1 Combine like terms: -1.018446878 + 1 = -0.018446878 n = -0.018446878 Simplifying n = -0.018446878Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.018446878, -0.018446878}
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