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Simplifying 5n2 + 39n + -28 = 0 Reorder the terms: -28 + 39n + 5n2 = 0 Solving -28 + 39n + 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'. -5.6 + 7.8n + n2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + 7.8n + 5.6 + n2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + 7.8n + n2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + 7.8n + n2 = 0 + 5.6 7.8n + n2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 7.8n + n2 = 5.6 The n term is 7.8n. Take half its coefficient (3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. 7.8n + 15.21 + n2 = 5.6 + 15.21 Reorder the terms: 15.21 + 7.8n + n2 = 5.6 + 15.21 Combine like terms: 5.6 + 15.21 = 20.81 15.21 + 7.8n + n2 = 20.81 Factor a perfect square on the left side: (n + 3.9)(n + 3.9) = 20.81 Calculate the square root of the right side: 4.561797891 Break this problem into two subproblems by setting (n + 3.9) equal to 4.561797891 and -4.561797891.Subproblem 1
n + 3.9 = 4.561797891 Simplifying n + 3.9 = 4.561797891 Reorder the terms: 3.9 + n = 4.561797891 Solving 3.9 + n = 4.561797891 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + n = 4.561797891 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + n = 4.561797891 + -3.9 n = 4.561797891 + -3.9 Combine like terms: 4.561797891 + -3.9 = 0.661797891 n = 0.661797891 Simplifying n = 0.661797891Subproblem 2
n + 3.9 = -4.561797891 Simplifying n + 3.9 = -4.561797891 Reorder the terms: 3.9 + n = -4.561797891 Solving 3.9 + n = -4.561797891 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + n = -4.561797891 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + n = -4.561797891 + -3.9 n = -4.561797891 + -3.9 Combine like terms: -4.561797891 + -3.9 = -8.461797891 n = -8.461797891 Simplifying n = -8.461797891Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.661797891, -8.461797891}
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