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Simplifying (n + -1)(n + -12) = 7n Reorder the terms: (-1 + n)(n + -12) = 7n Reorder the terms: (-1 + n)(-12 + n) = 7n Multiply (-1 + n) * (-12 + n) (-1(-12 + n) + n(-12 + n)) = 7n ((-12 * -1 + n * -1) + n(-12 + n)) = 7n ((12 + -1n) + n(-12 + n)) = 7n (12 + -1n + (-12 * n + n * n)) = 7n (12 + -1n + (-12n + n2)) = 7n Combine like terms: -1n + -12n = -13n (12 + -13n + n2) = 7n Solving 12 + -13n + n2 = 7n Solving for variable 'n'. Reorder the terms: 12 + -13n + -7n + n2 = 7n + -7n Combine like terms: -13n + -7n = -20n 12 + -20n + n2 = 7n + -7n Combine like terms: 7n + -7n = 0 12 + -20n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -20n + -12 + n2 = 0 + -12 Reorder the terms: 12 + -12 + -20n + n2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -20n + n2 = 0 + -12 -20n + n2 = 0 + -12 Combine like terms: 0 + -12 = -12 -20n + n2 = -12 The n term is -20n. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20n + 100 + n2 = -12 + 100 Reorder the terms: 100 + -20n + n2 = -12 + 100 Combine like terms: -12 + 100 = 88 100 + -20n + n2 = 88 Factor a perfect square on the left side: (n + -10)(n + -10) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (n + -10) equal to 9.38083152 and -9.38083152.Subproblem 1
n + -10 = 9.38083152 Simplifying n + -10 = 9.38083152 Reorder the terms: -10 + n = 9.38083152 Solving -10 + n = 9.38083152 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + n = 9.38083152 + 10 Combine like terms: -10 + 10 = 0 0 + n = 9.38083152 + 10 n = 9.38083152 + 10 Combine like terms: 9.38083152 + 10 = 19.38083152 n = 19.38083152 Simplifying n = 19.38083152Subproblem 2
n + -10 = -9.38083152 Simplifying n + -10 = -9.38083152 Reorder the terms: -10 + n = -9.38083152 Solving -10 + n = -9.38083152 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + n = -9.38083152 + 10 Combine like terms: -10 + 10 = 0 0 + n = -9.38083152 + 10 n = -9.38083152 + 10 Combine like terms: -9.38083152 + 10 = 0.61916848 n = 0.61916848 Simplifying n = 0.61916848Solution
The solution to the problem is based on the solutions from the subproblems. n = {19.38083152, 0.61916848}
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