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Simplifying 5n2 + -38 + -15n = 0 Reorder the terms: -38 + -15n + 5n2 = 0 Solving -38 + -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'. -7.6 + -3n + n2 = 0 Move the constant term to the right: Add '7.6' to each side of the equation. -7.6 + -3n + 7.6 + n2 = 0 + 7.6 Reorder the terms: -7.6 + 7.6 + -3n + n2 = 0 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + -3n + n2 = 0 + 7.6 -3n + n2 = 0 + 7.6 Combine like terms: 0 + 7.6 = 7.6 -3n + n2 = 7.6 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 = 7.6 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 7.6 + 2.25 Combine like terms: 7.6 + 2.25 = 9.85 2.25 + -3n + n2 = 9.85 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 9.85 Calculate the square root of the right side: 3.138470965 Break this problem into two subproblems by setting (n + -1.5) equal to 3.138470965 and -3.138470965.Subproblem 1
n + -1.5 = 3.138470965 Simplifying n + -1.5 = 3.138470965 Reorder the terms: -1.5 + n = 3.138470965 Solving -1.5 + n = 3.138470965 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 = 3.138470965 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 3.138470965 + 1.5 n = 3.138470965 + 1.5 Combine like terms: 3.138470965 + 1.5 = 4.638470965 n = 4.638470965 Simplifying n = 4.638470965Subproblem 2
n + -1.5 = -3.138470965 Simplifying n + -1.5 = -3.138470965 Reorder the terms: -1.5 + n = -3.138470965 Solving -1.5 + n = -3.138470965 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 = -3.138470965 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -3.138470965 + 1.5 n = -3.138470965 + 1.5 Combine like terms: -3.138470965 + 1.5 = -1.638470965 n = -1.638470965 Simplifying n = -1.638470965Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.638470965, -1.638470965}
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