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Simplifying -2n2 + 4n = -7 Reorder the terms: 4n + -2n2 = -7 Solving 4n + -2n2 = -7 Solving for variable 'n'. Reorder the terms: 7 + 4n + -2n2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 4n + -2n2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3.5 + -2n + n2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -2n + 3.5 + n2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -2n + n2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -2n + n2 = 0 + 3.5 -2n + n2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -2n + n2 = 3.5 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 3.5 + 1 Reorder the terms: 1 + -2n + n2 = 3.5 + 1 Combine like terms: 3.5 + 1 = 4.5 1 + -2n + n2 = 4.5 Factor a perfect square on the left side: (n + -1)(n + -1) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (n + -1) equal to 2.121320344 and -2.121320344.Subproblem 1
n + -1 = 2.121320344 Simplifying n + -1 = 2.121320344 Reorder the terms: -1 + n = 2.121320344 Solving -1 + n = 2.121320344 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 2.121320344 + 1 Combine like terms: -1 + 1 = 0 0 + n = 2.121320344 + 1 n = 2.121320344 + 1 Combine like terms: 2.121320344 + 1 = 3.121320344 n = 3.121320344 Simplifying n = 3.121320344Subproblem 2
n + -1 = -2.121320344 Simplifying n + -1 = -2.121320344 Reorder the terms: -1 + n = -2.121320344 Solving -1 + n = -2.121320344 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -2.121320344 + 1 Combine like terms: -1 + 1 = 0 0 + n = -2.121320344 + 1 n = -2.121320344 + 1 Combine like terms: -2.121320344 + 1 = -1.121320344 n = -1.121320344 Simplifying n = -1.121320344Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.121320344, -1.121320344}
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