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Simplifying 5n2 + 21n + 20 = 0 Reorder the terms: 20 + 21n + 5n2 = 0 Solving 20 + 21n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4 + 4.2n + n2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 4.2n + -4 + n2 = 0 + -4 Reorder the terms: 4 + -4 + 4.2n + n2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 4.2n + n2 = 0 + -4 4.2n + n2 = 0 + -4 Combine like terms: 0 + -4 = -4 4.2n + n2 = -4 The n term is 4.2n. Take half its coefficient (2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. 4.2n + 4.41 + n2 = -4 + 4.41 Reorder the terms: 4.41 + 4.2n + n2 = -4 + 4.41 Combine like terms: -4 + 4.41 = 0.41 4.41 + 4.2n + n2 = 0.41 Factor a perfect square on the left side: (n + 2.1)(n + 2.1) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (n + 2.1) equal to 0.640312424 and -0.640312424.Subproblem 1
n + 2.1 = 0.640312424 Simplifying n + 2.1 = 0.640312424 Reorder the terms: 2.1 + n = 0.640312424 Solving 2.1 + n = 0.640312424 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + n = 0.640312424 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + n = 0.640312424 + -2.1 n = 0.640312424 + -2.1 Combine like terms: 0.640312424 + -2.1 = -1.459687576 n = -1.459687576 Simplifying n = -1.459687576Subproblem 2
n + 2.1 = -0.640312424 Simplifying n + 2.1 = -0.640312424 Reorder the terms: 2.1 + n = -0.640312424 Solving 2.1 + n = -0.640312424 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + n = -0.640312424 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + n = -0.640312424 + -2.1 n = -0.640312424 + -2.1 Combine like terms: -0.640312424 + -2.1 = -2.740312424 n = -2.740312424 Simplifying n = -2.740312424Solution
The solution to the problem is based on the solutions from the subproblems. n = {-1.459687576, -2.740312424}
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