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Simplifying 2n2 + -1n + -10 = 10 Reorder the terms: -10 + -1n + 2n2 = 10 Solving -10 + -1n + 2n2 = 10 Solving for variable 'n'. Reorder the terms: -10 + -10 + -1n + 2n2 = 10 + -10 Combine like terms: -10 + -10 = -20 -20 + -1n + 2n2 = 10 + -10 Combine like terms: 10 + -10 = 0 -20 + -1n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10 + -0.5n + n2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -0.5n + 10 + n2 = 0 + 10 Reorder the terms: -10 + 10 + -0.5n + n2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -0.5n + n2 = 0 + 10 -0.5n + n2 = 0 + 10 Combine like terms: 0 + 10 = 10 -0.5n + n2 = 10 The n term is -0.5n. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5n + 0.0625 + n2 = 10 + 0.0625 Reorder the terms: 0.0625 + -0.5n + n2 = 10 + 0.0625 Combine like terms: 10 + 0.0625 = 10.0625 0.0625 + -0.5n + n2 = 10.0625 Factor a perfect square on the left side: (n + -0.25)(n + -0.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (n + -0.25) equal to 3.172144385 and -3.172144385.Subproblem 1
n + -0.25 = 3.172144385 Simplifying n + -0.25 = 3.172144385 Reorder the terms: -0.25 + n = 3.172144385 Solving -0.25 + n = 3.172144385 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + n = 3.172144385 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + n = 3.172144385 + 0.25 n = 3.172144385 + 0.25 Combine like terms: 3.172144385 + 0.25 = 3.422144385 n = 3.422144385 Simplifying n = 3.422144385Subproblem 2
n + -0.25 = -3.172144385 Simplifying n + -0.25 = -3.172144385 Reorder the terms: -0.25 + n = -3.172144385 Solving -0.25 + n = -3.172144385 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + n = -3.172144385 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + n = -3.172144385 + 0.25 n = -3.172144385 + 0.25 Combine like terms: -3.172144385 + 0.25 = -2.922144385 n = -2.922144385 Simplifying n = -2.922144385Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.422144385, -2.922144385}
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