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Simplifying 5n2 + 9n + -910 = 0 Reorder the terms: -910 + 9n + 5n2 = 0 Solving -910 + 9n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -182 + 1.8n + n2 = 0 Move the constant term to the right: Add '182' to each side of the equation. -182 + 1.8n + 182 + n2 = 0 + 182 Reorder the terms: -182 + 182 + 1.8n + n2 = 0 + 182 Combine like terms: -182 + 182 = 0 0 + 1.8n + n2 = 0 + 182 1.8n + n2 = 0 + 182 Combine like terms: 0 + 182 = 182 1.8n + n2 = 182 The n term is 1.8n. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8n + 0.81 + n2 = 182 + 0.81 Reorder the terms: 0.81 + 1.8n + n2 = 182 + 0.81 Combine like terms: 182 + 0.81 = 182.81 0.81 + 1.8n + n2 = 182.81 Factor a perfect square on the left side: (n + 0.9)(n + 0.9) = 182.81 Calculate the square root of the right side: 13.520724833 Break this problem into two subproblems by setting (n + 0.9) equal to 13.520724833 and -13.520724833.Subproblem 1
n + 0.9 = 13.520724833 Simplifying n + 0.9 = 13.520724833 Reorder the terms: 0.9 + n = 13.520724833 Solving 0.9 + n = 13.520724833 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + n = 13.520724833 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + n = 13.520724833 + -0.9 n = 13.520724833 + -0.9 Combine like terms: 13.520724833 + -0.9 = 12.620724833 n = 12.620724833 Simplifying n = 12.620724833Subproblem 2
n + 0.9 = -13.520724833 Simplifying n + 0.9 = -13.520724833 Reorder the terms: 0.9 + n = -13.520724833 Solving 0.9 + n = -13.520724833 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + n = -13.520724833 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + n = -13.520724833 + -0.9 n = -13.520724833 + -0.9 Combine like terms: -13.520724833 + -0.9 = -14.420724833 n = -14.420724833 Simplifying n = -14.420724833Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.620724833, -14.420724833}
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