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Simplifying n2 + -4n + -22 = 0 Reorder the terms: -22 + -4n + n2 = 0 Solving -22 + -4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -4n + 22 + n2 = 0 + 22 Reorder the terms: -22 + 22 + -4n + n2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -4n + n2 = 0 + 22 -4n + n2 = 0 + 22 Combine like terms: 0 + 22 = 22 -4n + n2 = 22 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 22 + 4 Reorder the terms: 4 + -4n + n2 = 22 + 4 Combine like terms: 22 + 4 = 26 4 + -4n + n2 = 26 Factor a perfect square on the left side: (n + -2)(n + -2) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (n + -2) equal to 5.099019514 and -5.099019514.Subproblem 1
n + -2 = 5.099019514 Simplifying n + -2 = 5.099019514 Reorder the terms: -2 + n = 5.099019514 Solving -2 + n = 5.099019514 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 5.099019514 + 2 Combine like terms: -2 + 2 = 0 0 + n = 5.099019514 + 2 n = 5.099019514 + 2 Combine like terms: 5.099019514 + 2 = 7.099019514 n = 7.099019514 Simplifying n = 7.099019514Subproblem 2
n + -2 = -5.099019514 Simplifying n + -2 = -5.099019514 Reorder the terms: -2 + n = -5.099019514 Solving -2 + n = -5.099019514 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -5.099019514 + 2 Combine like terms: -2 + 2 = 0 0 + n = -5.099019514 + 2 n = -5.099019514 + 2 Combine like terms: -5.099019514 + 2 = -3.099019514 n = -3.099019514 Simplifying n = -3.099019514Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.099019514, -3.099019514}
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