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Simplifying (n + -3)(n + -3) = 250 Reorder the terms: (-3 + n)(n + -3) = 250 Reorder the terms: (-3 + n)(-3 + n) = 250 Multiply (-3 + n) * (-3 + n) (-3(-3 + n) + n(-3 + n)) = 250 ((-3 * -3 + n * -3) + n(-3 + n)) = 250 ((9 + -3n) + n(-3 + n)) = 250 (9 + -3n + (-3 * n + n * n)) = 250 (9 + -3n + (-3n + n2)) = 250 Combine like terms: -3n + -3n = -6n (9 + -6n + n2) = 250 Solving 9 + -6n + n2 = 250 Solving for variable 'n'. Reorder the terms: 9 + -250 + -6n + n2 = 250 + -250 Combine like terms: 9 + -250 = -241 -241 + -6n + n2 = 250 + -250 Combine like terms: 250 + -250 = 0 -241 + -6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '241' to each side of the equation. -241 + -6n + 241 + n2 = 0 + 241 Reorder the terms: -241 + 241 + -6n + n2 = 0 + 241 Combine like terms: -241 + 241 = 0 0 + -6n + n2 = 0 + 241 -6n + n2 = 0 + 241 Combine like terms: 0 + 241 = 241 -6n + n2 = 241 The n term is -6n. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n + 9 + n2 = 241 + 9 Reorder the terms: 9 + -6n + n2 = 241 + 9 Combine like terms: 241 + 9 = 250 9 + -6n + n2 = 250 Factor a perfect square on the left side: (n + -3)(n + -3) = 250 Calculate the square root of the right side: 15.811388301 Break this problem into two subproblems by setting (n + -3) equal to 15.811388301 and -15.811388301.Subproblem 1
n + -3 = 15.811388301 Simplifying n + -3 = 15.811388301 Reorder the terms: -3 + n = 15.811388301 Solving -3 + n = 15.811388301 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = 15.811388301 + 3 Combine like terms: -3 + 3 = 0 0 + n = 15.811388301 + 3 n = 15.811388301 + 3 Combine like terms: 15.811388301 + 3 = 18.811388301 n = 18.811388301 Simplifying n = 18.811388301Subproblem 2
n + -3 = -15.811388301 Simplifying n + -3 = -15.811388301 Reorder the terms: -3 + n = -15.811388301 Solving -3 + n = -15.811388301 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = -15.811388301 + 3 Combine like terms: -3 + 3 = 0 0 + n = -15.811388301 + 3 n = -15.811388301 + 3 Combine like terms: -15.811388301 + 3 = -12.811388301 n = -12.811388301 Simplifying n = -12.811388301Solution
The solution to the problem is based on the solutions from the subproblems. n = {18.811388301, -12.811388301}
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