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Simplifying 8n2 + 7n + -22 = 0 Reorder the terms: -22 + 7n + 8n2 = 0 Solving -22 + 7n + 8n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.75 + 0.875n + n2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 0.875n + 2.75 + n2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 0.875n + n2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 0.875n + n2 = 0 + 2.75 0.875n + n2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 0.875n + n2 = 2.75 The n term is 0.875n. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875n + 0.19140625 + n2 = 2.75 + 0.19140625 Reorder the terms: 0.19140625 + 0.875n + n2 = 2.75 + 0.19140625 Combine like terms: 2.75 + 0.19140625 = 2.94140625 0.19140625 + 0.875n + n2 = 2.94140625 Factor a perfect square on the left side: (n + 0.4375)(n + 0.4375) = 2.94140625 Calculate the square root of the right side: 1.715052842 Break this problem into two subproblems by setting (n + 0.4375) equal to 1.715052842 and -1.715052842.Subproblem 1
n + 0.4375 = 1.715052842 Simplifying n + 0.4375 = 1.715052842 Reorder the terms: 0.4375 + n = 1.715052842 Solving 0.4375 + n = 1.715052842 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + n = 1.715052842 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + n = 1.715052842 + -0.4375 n = 1.715052842 + -0.4375 Combine like terms: 1.715052842 + -0.4375 = 1.277552842 n = 1.277552842 Simplifying n = 1.277552842Subproblem 2
n + 0.4375 = -1.715052842 Simplifying n + 0.4375 = -1.715052842 Reorder the terms: 0.4375 + n = -1.715052842 Solving 0.4375 + n = -1.715052842 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + n = -1.715052842 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + n = -1.715052842 + -0.4375 n = -1.715052842 + -0.4375 Combine like terms: -1.715052842 + -0.4375 = -2.152552842 n = -2.152552842 Simplifying n = -2.152552842Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.277552842, -2.152552842}
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