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Simplifying 2n2 + -7n + -13 = -10 Reorder the terms: -13 + -7n + 2n2 = -10 Solving -13 + -7n + 2n2 = -10 Solving for variable 'n'. Reorder the terms: -13 + 10 + -7n + 2n2 = -10 + 10 Combine like terms: -13 + 10 = -3 -3 + -7n + 2n2 = -10 + 10 Combine like terms: -10 + 10 = 0 -3 + -7n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -3.5n + n2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -3.5n + 1.5 + n2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -3.5n + n2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -3.5n + n2 = 0 + 1.5 -3.5n + n2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -3.5n + n2 = 1.5 The n term is -3.5n. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5n + 3.0625 + n2 = 1.5 + 3.0625 Reorder the terms: 3.0625 + -3.5n + n2 = 1.5 + 3.0625 Combine like terms: 1.5 + 3.0625 = 4.5625 3.0625 + -3.5n + n2 = 4.5625 Factor a perfect square on the left side: (n + -1.75)(n + -1.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (n + -1.75) equal to 2.136000936 and -2.136000936.Subproblem 1
n + -1.75 = 2.136000936 Simplifying n + -1.75 = 2.136000936 Reorder the terms: -1.75 + n = 2.136000936 Solving -1.75 + n = 2.136000936 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + n = 2.136000936 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + n = 2.136000936 + 1.75 n = 2.136000936 + 1.75 Combine like terms: 2.136000936 + 1.75 = 3.886000936 n = 3.886000936 Simplifying n = 3.886000936Subproblem 2
n + -1.75 = -2.136000936 Simplifying n + -1.75 = -2.136000936 Reorder the terms: -1.75 + n = -2.136000936 Solving -1.75 + n = -2.136000936 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + n = -2.136000936 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + n = -2.136000936 + 1.75 n = -2.136000936 + 1.75 Combine like terms: -2.136000936 + 1.75 = -0.386000936 n = -0.386000936 Simplifying n = -0.386000936Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.886000936, -0.386000936}
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