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Simplifying n2 + -4n + -47 = 0 Reorder the terms: -47 + -4n + n2 = 0 Solving -47 + -4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -4n + 47 + n2 = 0 + 47 Reorder the terms: -47 + 47 + -4n + n2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -4n + n2 = 0 + 47 -4n + n2 = 0 + 47 Combine like terms: 0 + 47 = 47 -4n + n2 = 47 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 = 47 + 4 Reorder the terms: 4 + -4n + n2 = 47 + 4 Combine like terms: 47 + 4 = 51 4 + -4n + n2 = 51 Factor a perfect square on the left side: (n + -2)(n + -2) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (n + -2) equal to 7.141428429 and -7.141428429.Subproblem 1
n + -2 = 7.141428429 Simplifying n + -2 = 7.141428429 Reorder the terms: -2 + n = 7.141428429 Solving -2 + n = 7.141428429 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 = 7.141428429 + 2 Combine like terms: -2 + 2 = 0 0 + n = 7.141428429 + 2 n = 7.141428429 + 2 Combine like terms: 7.141428429 + 2 = 9.141428429 n = 9.141428429 Simplifying n = 9.141428429Subproblem 2
n + -2 = -7.141428429 Simplifying n + -2 = -7.141428429 Reorder the terms: -2 + n = -7.141428429 Solving -2 + n = -7.141428429 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 = -7.141428429 + 2 Combine like terms: -2 + 2 = 0 0 + n = -7.141428429 + 2 n = -7.141428429 + 2 Combine like terms: -7.141428429 + 2 = -5.141428429 n = -5.141428429 Simplifying n = -5.141428429Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.141428429, -5.141428429}
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