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Simplifying 5n2 + -45n + 11 = 0 Reorder the terms: 11 + -45n + 5n2 = 0 Solving 11 + -45n + 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'. 2.2 + -9n + n2 = 0 Move the constant term to the right: Add '-2.2' to each side of the equation. 2.2 + -9n + -2.2 + n2 = 0 + -2.2 Reorder the terms: 2.2 + -2.2 + -9n + n2 = 0 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + -9n + n2 = 0 + -2.2 -9n + n2 = 0 + -2.2 Combine like terms: 0 + -2.2 = -2.2 -9n + n2 = -2.2 The n term is -9n. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9n + 20.25 + n2 = -2.2 + 20.25 Reorder the terms: 20.25 + -9n + n2 = -2.2 + 20.25 Combine like terms: -2.2 + 20.25 = 18.05 20.25 + -9n + n2 = 18.05 Factor a perfect square on the left side: (n + -4.5)(n + -4.5) = 18.05 Calculate the square root of the right side: 4.248529157 Break this problem into two subproblems by setting (n + -4.5) equal to 4.248529157 and -4.248529157.Subproblem 1
n + -4.5 = 4.248529157 Simplifying n + -4.5 = 4.248529157 Reorder the terms: -4.5 + n = 4.248529157 Solving -4.5 + n = 4.248529157 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = 4.248529157 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = 4.248529157 + 4.5 n = 4.248529157 + 4.5 Combine like terms: 4.248529157 + 4.5 = 8.748529157 n = 8.748529157 Simplifying n = 8.748529157Subproblem 2
n + -4.5 = -4.248529157 Simplifying n + -4.5 = -4.248529157 Reorder the terms: -4.5 + n = -4.248529157 Solving -4.5 + n = -4.248529157 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = -4.248529157 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = -4.248529157 + 4.5 n = -4.248529157 + 4.5 Combine like terms: -4.248529157 + 4.5 = 0.251470843 n = 0.251470843 Simplifying n = 0.251470843Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.748529157, 0.251470843}
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