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Simplifying 2n2 + 11n + 10 = 0 Reorder the terms: 10 + 11n + 2n2 = 0 Solving 10 + 11n + 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'. 5 + 5.5n + n2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 5.5n + -5 + n2 = 0 + -5 Reorder the terms: 5 + -5 + 5.5n + n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 5.5n + n2 = 0 + -5 5.5n + n2 = 0 + -5 Combine like terms: 0 + -5 = -5 5.5n + n2 = -5 The n term is 5.5n. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5n + 7.5625 + n2 = -5 + 7.5625 Reorder the terms: 7.5625 + 5.5n + n2 = -5 + 7.5625 Combine like terms: -5 + 7.5625 = 2.5625 7.5625 + 5.5n + n2 = 2.5625 Factor a perfect square on the left side: (n + 2.75)(n + 2.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (n + 2.75) equal to 1.600781059 and -1.600781059.Subproblem 1
n + 2.75 = 1.600781059 Simplifying n + 2.75 = 1.600781059 Reorder the terms: 2.75 + n = 1.600781059 Solving 2.75 + n = 1.600781059 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + n = 1.600781059 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + n = 1.600781059 + -2.75 n = 1.600781059 + -2.75 Combine like terms: 1.600781059 + -2.75 = -1.149218941 n = -1.149218941 Simplifying n = -1.149218941Subproblem 2
n + 2.75 = -1.600781059 Simplifying n + 2.75 = -1.600781059 Reorder the terms: 2.75 + n = -1.600781059 Solving 2.75 + n = -1.600781059 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + n = -1.600781059 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + n = -1.600781059 + -2.75 n = -1.600781059 + -2.75 Combine like terms: -1.600781059 + -2.75 = -4.350781059 n = -4.350781059 Simplifying n = -4.350781059Solution
The solution to the problem is based on the solutions from the subproblems. n = {-1.149218941, -4.350781059}
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