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Simplifying 5n2 + 24n + -44 = 0 Reorder the terms: -44 + 24n + 5n2 = 0 Solving -44 + 24n + 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'. -8.8 + 4.8n + n2 = 0 Move the constant term to the right: Add '8.8' to each side of the equation. -8.8 + 4.8n + 8.8 + n2 = 0 + 8.8 Reorder the terms: -8.8 + 8.8 + 4.8n + n2 = 0 + 8.8 Combine like terms: -8.8 + 8.8 = 0.0 0.0 + 4.8n + n2 = 0 + 8.8 4.8n + n2 = 0 + 8.8 Combine like terms: 0 + 8.8 = 8.8 4.8n + n2 = 8.8 The n term is 4.8n. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8n + 5.76 + n2 = 8.8 + 5.76 Reorder the terms: 5.76 + 4.8n + n2 = 8.8 + 5.76 Combine like terms: 8.8 + 5.76 = 14.56 5.76 + 4.8n + n2 = 14.56 Factor a perfect square on the left side: (n + 2.4)(n + 2.4) = 14.56 Calculate the square root of the right side: 3.815756806 Break this problem into two subproblems by setting (n + 2.4) equal to 3.815756806 and -3.815756806.Subproblem 1
n + 2.4 = 3.815756806 Simplifying n + 2.4 = 3.815756806 Reorder the terms: 2.4 + n = 3.815756806 Solving 2.4 + n = 3.815756806 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + n = 3.815756806 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + n = 3.815756806 + -2.4 n = 3.815756806 + -2.4 Combine like terms: 3.815756806 + -2.4 = 1.415756806 n = 1.415756806 Simplifying n = 1.415756806Subproblem 2
n + 2.4 = -3.815756806 Simplifying n + 2.4 = -3.815756806 Reorder the terms: 2.4 + n = -3.815756806 Solving 2.4 + n = -3.815756806 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + n = -3.815756806 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + n = -3.815756806 + -2.4 n = -3.815756806 + -2.4 Combine like terms: -3.815756806 + -2.4 = -6.215756806 n = -6.215756806 Simplifying n = -6.215756806Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.415756806, -6.215756806}
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