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Simplifying 5n2 + 15n + -8 = 0 Reorder the terms: -8 + 15n + 5n2 = 0 Solving -8 + 15n + 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'. -1.6 + 3n + n2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 3n + 1.6 + n2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 3n + n2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 3n + n2 = 0 + 1.6 3n + n2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 3n + n2 = 1.6 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 = 1.6 + 2.25 Reorder the terms: 2.25 + 3n + n2 = 1.6 + 2.25 Combine like terms: 1.6 + 2.25 = 3.85 2.25 + 3n + n2 = 3.85 Factor a perfect square on the left side: (n + 1.5)(n + 1.5) = 3.85 Calculate the square root of the right side: 1.962141687 Break this problem into two subproblems by setting (n + 1.5) equal to 1.962141687 and -1.962141687.Subproblem 1
n + 1.5 = 1.962141687 Simplifying n + 1.5 = 1.962141687 Reorder the terms: 1.5 + n = 1.962141687 Solving 1.5 + n = 1.962141687 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 = 1.962141687 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = 1.962141687 + -1.5 n = 1.962141687 + -1.5 Combine like terms: 1.962141687 + -1.5 = 0.462141687 n = 0.462141687 Simplifying n = 0.462141687Subproblem 2
n + 1.5 = -1.962141687 Simplifying n + 1.5 = -1.962141687 Reorder the terms: 1.5 + n = -1.962141687 Solving 1.5 + n = -1.962141687 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 = -1.962141687 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = -1.962141687 + -1.5 n = -1.962141687 + -1.5 Combine like terms: -1.962141687 + -1.5 = -3.462141687 n = -3.462141687 Simplifying n = -3.462141687Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.462141687, -3.462141687}
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