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Simplifying 5n2 + -29n + -47 = 0 Reorder the terms: -47 + -29n + 5n2 = 0 Solving -47 + -29n + 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'. -9.4 + -5.8n + n2 = 0 Move the constant term to the right: Add '9.4' to each side of the equation. -9.4 + -5.8n + 9.4 + n2 = 0 + 9.4 Reorder the terms: -9.4 + 9.4 + -5.8n + n2 = 0 + 9.4 Combine like terms: -9.4 + 9.4 = 0.0 0.0 + -5.8n + n2 = 0 + 9.4 -5.8n + n2 = 0 + 9.4 Combine like terms: 0 + 9.4 = 9.4 -5.8n + n2 = 9.4 The n term is -5.8n. Take half its coefficient (-2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. -5.8n + 8.41 + n2 = 9.4 + 8.41 Reorder the terms: 8.41 + -5.8n + n2 = 9.4 + 8.41 Combine like terms: 9.4 + 8.41 = 17.81 8.41 + -5.8n + n2 = 17.81 Factor a perfect square on the left side: (n + -2.9)(n + -2.9) = 17.81 Calculate the square root of the right side: 4.220189569 Break this problem into two subproblems by setting (n + -2.9) equal to 4.220189569 and -4.220189569.Subproblem 1
n + -2.9 = 4.220189569 Simplifying n + -2.9 = 4.220189569 Reorder the terms: -2.9 + n = 4.220189569 Solving -2.9 + n = 4.220189569 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + n = 4.220189569 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + n = 4.220189569 + 2.9 n = 4.220189569 + 2.9 Combine like terms: 4.220189569 + 2.9 = 7.120189569 n = 7.120189569 Simplifying n = 7.120189569Subproblem 2
n + -2.9 = -4.220189569 Simplifying n + -2.9 = -4.220189569 Reorder the terms: -2.9 + n = -4.220189569 Solving -2.9 + n = -4.220189569 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + n = -4.220189569 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + n = -4.220189569 + 2.9 n = -4.220189569 + 2.9 Combine like terms: -4.220189569 + 2.9 = -1.320189569 n = -1.320189569 Simplifying n = -1.320189569Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.120189569, -1.320189569}
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