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Simplifying 2n2 + -143n + -390 = 0 Reorder the terms: -390 + -143n + 2n2 = 0 Solving -390 + -143n + 2n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -195 + -71.5n + n2 = 0 Move the constant term to the right: Add '195' to each side of the equation. -195 + -71.5n + 195 + n2 = 0 + 195 Reorder the terms: -195 + 195 + -71.5n + n2 = 0 + 195 Combine like terms: -195 + 195 = 0 0 + -71.5n + n2 = 0 + 195 -71.5n + n2 = 0 + 195 Combine like terms: 0 + 195 = 195 -71.5n + n2 = 195 The n term is -71.5n. Take half its coefficient (-35.75). Square it (1278.0625) and add it to both sides. Add '1278.0625' to each side of the equation. -71.5n + 1278.0625 + n2 = 195 + 1278.0625 Reorder the terms: 1278.0625 + -71.5n + n2 = 195 + 1278.0625 Combine like terms: 195 + 1278.0625 = 1473.0625 1278.0625 + -71.5n + n2 = 1473.0625 Factor a perfect square on the left side: (n + -35.75)(n + -35.75) = 1473.0625 Calculate the square root of the right side: 38.380496349 Break this problem into two subproblems by setting (n + -35.75) equal to 38.380496349 and -38.380496349.Subproblem 1
n + -35.75 = 38.380496349 Simplifying n + -35.75 = 38.380496349 Reorder the terms: -35.75 + n = 38.380496349 Solving -35.75 + n = 38.380496349 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '35.75' to each side of the equation. -35.75 + 35.75 + n = 38.380496349 + 35.75 Combine like terms: -35.75 + 35.75 = 0.00 0.00 + n = 38.380496349 + 35.75 n = 38.380496349 + 35.75 Combine like terms: 38.380496349 + 35.75 = 74.130496349 n = 74.130496349 Simplifying n = 74.130496349Subproblem 2
n + -35.75 = -38.380496349 Simplifying n + -35.75 = -38.380496349 Reorder the terms: -35.75 + n = -38.380496349 Solving -35.75 + n = -38.380496349 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '35.75' to each side of the equation. -35.75 + 35.75 + n = -38.380496349 + 35.75 Combine like terms: -35.75 + 35.75 = 0.00 0.00 + n = -38.380496349 + 35.75 n = -38.380496349 + 35.75 Combine like terms: -38.380496349 + 35.75 = -2.630496349 n = -2.630496349 Simplifying n = -2.630496349Solution
The solution to the problem is based on the solutions from the subproblems. n = {74.130496349, -2.630496349}
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