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Simplifying -7n(1n + -3) = -4 Reorder the terms: -7n(-3 + 1n) = -4 (-3 * -7n + 1n * -7n) = -4 (21n + -7n2) = -4 Solving 21n + -7n2 = -4 Solving for variable 'n'. Reorder the terms: 4 + 21n + -7n2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 21n + -7n2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.5714285714 + -3n + n2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -3n + 0.5714285714 + n2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -3n + n2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -3n + n2 = 0 + 0.5714285714 -3n + n2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -3n + n2 = 0.5714285714 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 0.5714285714 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 0.5714285714 + 2.25 Combine like terms: 0.5714285714 + 2.25 = 2.8214285714 2.25 + -3n + n2 = 2.8214285714 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 2.8214285714 Calculate the square root of the right side: 1.679710859 Break this problem into two subproblems by setting (n + -1.5) equal to 1.679710859 and -1.679710859.Subproblem 1
n + -1.5 = 1.679710859 Simplifying n + -1.5 = 1.679710859 Reorder the terms: -1.5 + n = 1.679710859 Solving -1.5 + n = 1.679710859 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 1.679710859 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 1.679710859 + 1.5 n = 1.679710859 + 1.5 Combine like terms: 1.679710859 + 1.5 = 3.179710859 n = 3.179710859 Simplifying n = 3.179710859Subproblem 2
n + -1.5 = -1.679710859 Simplifying n + -1.5 = -1.679710859 Reorder the terms: -1.5 + n = -1.679710859 Solving -1.5 + n = -1.679710859 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -1.679710859 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -1.679710859 + 1.5 n = -1.679710859 + 1.5 Combine like terms: -1.679710859 + 1.5 = -0.179710859 n = -0.179710859 Simplifying n = -0.179710859Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.179710859, -0.179710859}
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