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Simplifying 5n2 + 29n + -22 = 0 Reorder the terms: -22 + 29n + 5n2 = 0 Solving -22 + 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'. -4.4 + 5.8n + n2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + 5.8n + 4.4 + n2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + 5.8n + n2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + 5.8n + n2 = 0 + 4.4 5.8n + n2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 5.8n + n2 = 4.4 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 = 4.4 + 8.41 Reorder the terms: 8.41 + 5.8n + n2 = 4.4 + 8.41 Combine like terms: 4.4 + 8.41 = 12.81 8.41 + 5.8n + n2 = 12.81 Factor a perfect square on the left side: (n + 2.9)(n + 2.9) = 12.81 Calculate the square root of the right side: 3.579106034 Break this problem into two subproblems by setting (n + 2.9) equal to 3.579106034 and -3.579106034.Subproblem 1
n + 2.9 = 3.579106034 Simplifying n + 2.9 = 3.579106034 Reorder the terms: 2.9 + n = 3.579106034 Solving 2.9 + n = 3.579106034 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 = 3.579106034 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + n = 3.579106034 + -2.9 n = 3.579106034 + -2.9 Combine like terms: 3.579106034 + -2.9 = 0.679106034 n = 0.679106034 Simplifying n = 0.679106034Subproblem 2
n + 2.9 = -3.579106034 Simplifying n + 2.9 = -3.579106034 Reorder the terms: 2.9 + n = -3.579106034 Solving 2.9 + n = -3.579106034 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 = -3.579106034 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + n = -3.579106034 + -2.9 n = -3.579106034 + -2.9 Combine like terms: -3.579106034 + -2.9 = -6.479106034 n = -6.479106034 Simplifying n = -6.479106034Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.679106034, -6.479106034}
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