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Simplifying 2n2 + 4n = 17 Reorder the terms: 4n + 2n2 = 17 Solving 4n + 2n2 = 17 Solving for variable 'n'. Reorder the terms: -17 + 4n + 2n2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 4n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.5 + 2n + n2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + 2n + 8.5 + n2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + 2n + n2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + 2n + n2 = 0 + 8.5 2n + n2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 2n + n2 = 8.5 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 = 8.5 + 1 Reorder the terms: 1 + 2n + n2 = 8.5 + 1 Combine like terms: 8.5 + 1 = 9.5 1 + 2n + n2 = 9.5 Factor a perfect square on the left side: (n + 1)(n + 1) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (n + 1) equal to 3.082207001 and -3.082207001.Subproblem 1
n + 1 = 3.082207001 Simplifying n + 1 = 3.082207001 Reorder the terms: 1 + n = 3.082207001 Solving 1 + n = 3.082207001 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 = 3.082207001 + -1 Combine like terms: 1 + -1 = 0 0 + n = 3.082207001 + -1 n = 3.082207001 + -1 Combine like terms: 3.082207001 + -1 = 2.082207001 n = 2.082207001 Simplifying n = 2.082207001Subproblem 2
n + 1 = -3.082207001 Simplifying n + 1 = -3.082207001 Reorder the terms: 1 + n = -3.082207001 Solving 1 + n = -3.082207001 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 = -3.082207001 + -1 Combine like terms: 1 + -1 = 0 0 + n = -3.082207001 + -1 n = -3.082207001 + -1 Combine like terms: -3.082207001 + -1 = -4.082207001 n = -4.082207001 Simplifying n = -4.082207001Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.082207001, -4.082207001}
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