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Simplifying 5n * n = 7 + -1n Multiply n * n 5n2 = 7 + -1n Solving 5n2 = 7 + -1n Solving for variable 'n'. Reorder the terms: -7 + n + 5n2 = 7 + -1n + -7 + n Reorder the terms: -7 + n + 5n2 = 7 + -7 + -1n + n Combine like terms: 7 + -7 = 0 -7 + n + 5n2 = 0 + -1n + n -7 + n + 5n2 = -1n + n Combine like terms: -1n + n = 0 -7 + n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 0.2n + n2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 0.2n + 1.4 + n2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 0.2n + n2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 0.2n + n2 = 0 + 1.4 0.2n + n2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 0.2n + n2 = 1.4 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. 0.2n + 0.25 + n2 = 1.4 + 0.25 Reorder the terms: 0.25 + 0.2n + n2 = 1.4 + 0.25 Combine like terms: 1.4 + 0.25 = 1.65 0.25 + 0.2n + n2 = 1.65 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 1.65 Calculate the square root of the right side: 1.284523258 Break this problem into two subproblems by setting (n + 0.5) equal to 1.284523258 and -1.284523258.Subproblem 1
n + 0.5 = 1.284523258 Simplifying n + 0.5 = 1.284523258 Reorder the terms: 0.5 + n = 1.284523258 Solving 0.5 + n = 1.284523258 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 = 1.284523258 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 1.284523258 + -0.5 n = 1.284523258 + -0.5 Combine like terms: 1.284523258 + -0.5 = 0.784523258 n = 0.784523258 Simplifying n = 0.784523258Subproblem 2
n + 0.5 = -1.284523258 Simplifying n + 0.5 = -1.284523258 Reorder the terms: 0.5 + n = -1.284523258 Solving 0.5 + n = -1.284523258 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 = -1.284523258 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -1.284523258 + -0.5 n = -1.284523258 + -0.5 Combine like terms: -1.284523258 + -0.5 = -1.784523258 n = -1.784523258 Simplifying n = -1.784523258Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.784523258, -1.784523258}
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