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Simplifying (n + 3)(n + -7) = 4 Reorder the terms: (3 + n)(n + -7) = 4 Reorder the terms: (3 + n)(-7 + n) = 4 Multiply (3 + n) * (-7 + n) (3(-7 + n) + n(-7 + n)) = 4 ((-7 * 3 + n * 3) + n(-7 + n)) = 4 ((-21 + 3n) + n(-7 + n)) = 4 (-21 + 3n + (-7 * n + n * n)) = 4 (-21 + 3n + (-7n + n2)) = 4 Combine like terms: 3n + -7n = -4n (-21 + -4n + n2) = 4 Solving -21 + -4n + n2 = 4 Solving for variable 'n'. Reorder the terms: -21 + -4 + -4n + n2 = 4 + -4 Combine like terms: -21 + -4 = -25 -25 + -4n + n2 = 4 + -4 Combine like terms: 4 + -4 = 0 -25 + -4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -4n + 25 + n2 = 0 + 25 Reorder the terms: -25 + 25 + -4n + n2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -4n + n2 = 0 + 25 -4n + n2 = 0 + 25 Combine like terms: 0 + 25 = 25 -4n + n2 = 25 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 = 25 + 4 Reorder the terms: 4 + -4n + n2 = 25 + 4 Combine like terms: 25 + 4 = 29 4 + -4n + n2 = 29 Factor a perfect square on the left side: (n + -2)(n + -2) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (n + -2) equal to 5.385164807 and -5.385164807.Subproblem 1
n + -2 = 5.385164807 Simplifying n + -2 = 5.385164807 Reorder the terms: -2 + n = 5.385164807 Solving -2 + n = 5.385164807 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 = 5.385164807 + 2 Combine like terms: -2 + 2 = 0 0 + n = 5.385164807 + 2 n = 5.385164807 + 2 Combine like terms: 5.385164807 + 2 = 7.385164807 n = 7.385164807 Simplifying n = 7.385164807Subproblem 2
n + -2 = -5.385164807 Simplifying n + -2 = -5.385164807 Reorder the terms: -2 + n = -5.385164807 Solving -2 + n = -5.385164807 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 = -5.385164807 + 2 Combine like terms: -2 + 2 = 0 0 + n = -5.385164807 + 2 n = -5.385164807 + 2 Combine like terms: -5.385164807 + 2 = -3.385164807 n = -3.385164807 Simplifying n = -3.385164807Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.385164807, -3.385164807}
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