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Simplifying n2 + -4 = 11n Reorder the terms: -4 + n2 = 11n Solving -4 + n2 = 11n Solving for variable 'n'. Reorder the terms: -4 + -11n + n2 = 11n + -11n Combine like terms: 11n + -11n = 0 -4 + -11n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -11n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + -11n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -11n + n2 = 0 + 4 -11n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 -11n + n2 = 4 The n term is -11n. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11n + 30.25 + n2 = 4 + 30.25 Reorder the terms: 30.25 + -11n + n2 = 4 + 30.25 Combine like terms: 4 + 30.25 = 34.25 30.25 + -11n + n2 = 34.25 Factor a perfect square on the left side: (n + -5.5)(n + -5.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (n + -5.5) equal to 5.852349955 and -5.852349955.Subproblem 1
n + -5.5 = 5.852349955 Simplifying n + -5.5 = 5.852349955 Reorder the terms: -5.5 + n = 5.852349955 Solving -5.5 + n = 5.852349955 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = 5.852349955 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = 5.852349955 + 5.5 n = 5.852349955 + 5.5 Combine like terms: 5.852349955 + 5.5 = 11.352349955 n = 11.352349955 Simplifying n = 11.352349955Subproblem 2
n + -5.5 = -5.852349955 Simplifying n + -5.5 = -5.852349955 Reorder the terms: -5.5 + n = -5.852349955 Solving -5.5 + n = -5.852349955 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = -5.852349955 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = -5.852349955 + 5.5 n = -5.852349955 + 5.5 Combine like terms: -5.852349955 + 5.5 = -0.352349955 n = -0.352349955 Simplifying n = -0.352349955Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.352349955, -0.352349955}
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