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Simplifying 20n2 + -18n + -5 = 0 Reorder the terms: -5 + -18n + 20n2 = 0 Solving -5 + -18n + 20n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.25 + -0.9n + n2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.9n + 0.25 + n2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.9n + n2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.9n + n2 = 0 + 0.25 -0.9n + n2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.9n + n2 = 0.25 The n term is -0.9n. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9n + 0.2025 + n2 = 0.25 + 0.2025 Reorder the terms: 0.2025 + -0.9n + n2 = 0.25 + 0.2025 Combine like terms: 0.25 + 0.2025 = 0.4525 0.2025 + -0.9n + n2 = 0.4525 Factor a perfect square on the left side: (n + -0.45)(n + -0.45) = 0.4525 Calculate the square root of the right side: 0.672681202 Break this problem into two subproblems by setting (n + -0.45) equal to 0.672681202 and -0.672681202.Subproblem 1
n + -0.45 = 0.672681202 Simplifying n + -0.45 = 0.672681202 Reorder the terms: -0.45 + n = 0.672681202 Solving -0.45 + n = 0.672681202 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + n = 0.672681202 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + n = 0.672681202 + 0.45 n = 0.672681202 + 0.45 Combine like terms: 0.672681202 + 0.45 = 1.122681202 n = 1.122681202 Simplifying n = 1.122681202Subproblem 2
n + -0.45 = -0.672681202 Simplifying n + -0.45 = -0.672681202 Reorder the terms: -0.45 + n = -0.672681202 Solving -0.45 + n = -0.672681202 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + n = -0.672681202 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + n = -0.672681202 + 0.45 n = -0.672681202 + 0.45 Combine like terms: -0.672681202 + 0.45 = -0.222681202 n = -0.222681202 Simplifying n = -0.222681202Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.122681202, -0.222681202}
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