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Simplifying 2n2 + 7n + -14 = 0 Reorder the terms: -14 + 7n + 2n2 = 0 Solving -14 + 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'. -7 + 3.5n + n2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 3.5n + 7 + n2 = 0 + 7 Reorder the terms: -7 + 7 + 3.5n + n2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3.5n + n2 = 0 + 7 3.5n + n2 = 0 + 7 Combine like terms: 0 + 7 = 7 3.5n + n2 = 7 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 = 7 + 3.0625 Reorder the terms: 3.0625 + 3.5n + n2 = 7 + 3.0625 Combine like terms: 7 + 3.0625 = 10.0625 3.0625 + 3.5n + n2 = 10.0625 Factor a perfect square on the left side: (n + 1.75)(n + 1.75) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (n + 1.75) equal to 3.172144385 and -3.172144385.Subproblem 1
n + 1.75 = 3.172144385 Simplifying n + 1.75 = 3.172144385 Reorder the terms: 1.75 + n = 3.172144385 Solving 1.75 + n = 3.172144385 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 = 3.172144385 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + n = 3.172144385 + -1.75 n = 3.172144385 + -1.75 Combine like terms: 3.172144385 + -1.75 = 1.422144385 n = 1.422144385 Simplifying n = 1.422144385Subproblem 2
n + 1.75 = -3.172144385 Simplifying n + 1.75 = -3.172144385 Reorder the terms: 1.75 + n = -3.172144385 Solving 1.75 + n = -3.172144385 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 = -3.172144385 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + n = -3.172144385 + -1.75 n = -3.172144385 + -1.75 Combine like terms: -3.172144385 + -1.75 = -4.922144385 n = -4.922144385 Simplifying n = -4.922144385Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.422144385, -4.922144385}
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