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Simplifying -2n2 + 7n + -2 = 0 Reorder the terms: -2 + 7n + -2n2 = 0 Solving -2 + 7n + -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'. 1 + -3.5n + n2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -3.5n + -1 + n2 = 0 + -1 Reorder the terms: 1 + -1 + -3.5n + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3.5n + n2 = 0 + -1 -3.5n + n2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3.5n + n2 = -1 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 + 3.0625 Reorder the terms: 3.0625 + -3.5n + n2 = -1 + 3.0625 Combine like terms: -1 + 3.0625 = 2.0625 3.0625 + -3.5n + n2 = 2.0625 Factor a perfect square on the left side: (n + -1.75)(n + -1.75) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (n + -1.75) equal to 1.436140662 and -1.436140662.Subproblem 1
n + -1.75 = 1.436140662 Simplifying n + -1.75 = 1.436140662 Reorder the terms: -1.75 + n = 1.436140662 Solving -1.75 + n = 1.436140662 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 = 1.436140662 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + n = 1.436140662 + 1.75 n = 1.436140662 + 1.75 Combine like terms: 1.436140662 + 1.75 = 3.186140662 n = 3.186140662 Simplifying n = 3.186140662Subproblem 2
n + -1.75 = -1.436140662 Simplifying n + -1.75 = -1.436140662 Reorder the terms: -1.75 + n = -1.436140662 Solving -1.75 + n = -1.436140662 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 = -1.436140662 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + n = -1.436140662 + 1.75 n = -1.436140662 + 1.75 Combine like terms: -1.436140662 + 1.75 = 0.313859338 n = 0.313859338 Simplifying n = 0.313859338Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.186140662, 0.313859338}
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