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Simplifying n2 + -4n + -39 = 7 Reorder the terms: -39 + -4n + n2 = 7 Solving -39 + -4n + n2 = 7 Solving for variable 'n'. Reorder the terms: -39 + -7 + -4n + n2 = 7 + -7 Combine like terms: -39 + -7 = -46 -46 + -4n + n2 = 7 + -7 Combine like terms: 7 + -7 = 0 -46 + -4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + -4n + 46 + n2 = 0 + 46 Reorder the terms: -46 + 46 + -4n + n2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -4n + n2 = 0 + 46 -4n + n2 = 0 + 46 Combine like terms: 0 + 46 = 46 -4n + n2 = 46 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 = 46 + 4 Reorder the terms: 4 + -4n + n2 = 46 + 4 Combine like terms: 46 + 4 = 50 4 + -4n + n2 = 50 Factor a perfect square on the left side: (n + -2)(n + -2) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (n + -2) equal to 7.071067812 and -7.071067812.Subproblem 1
n + -2 = 7.071067812 Simplifying n + -2 = 7.071067812 Reorder the terms: -2 + n = 7.071067812 Solving -2 + n = 7.071067812 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 = 7.071067812 + 2 Combine like terms: -2 + 2 = 0 0 + n = 7.071067812 + 2 n = 7.071067812 + 2 Combine like terms: 7.071067812 + 2 = 9.071067812 n = 9.071067812 Simplifying n = 9.071067812Subproblem 2
n + -2 = -7.071067812 Simplifying n + -2 = -7.071067812 Reorder the terms: -2 + n = -7.071067812 Solving -2 + n = -7.071067812 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 = -7.071067812 + 2 Combine like terms: -2 + 2 = 0 0 + n = -7.071067812 + 2 n = -7.071067812 + 2 Combine like terms: -7.071067812 + 2 = -5.071067812 n = -5.071067812 Simplifying n = -5.071067812Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.071067812, -5.071067812}
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