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Simplifying n2 + -3n + -12 = 0 Reorder the terms: -12 + -3n + n2 = 0 Solving -12 + -3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -3n + 12 + n2 = 0 + 12 Reorder the terms: -12 + 12 + -3n + n2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -3n + n2 = 0 + 12 -3n + n2 = 0 + 12 Combine like terms: 0 + 12 = 12 -3n + n2 = 12 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 12 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 12 + 2.25 Combine like terms: 12 + 2.25 = 14.25 2.25 + -3n + n2 = 14.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (n + -1.5) equal to 3.774917218 and -3.774917218.Subproblem 1
n + -1.5 = 3.774917218 Simplifying n + -1.5 = 3.774917218 Reorder the terms: -1.5 + n = 3.774917218 Solving -1.5 + n = 3.774917218 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 3.774917218 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 3.774917218 + 1.5 n = 3.774917218 + 1.5 Combine like terms: 3.774917218 + 1.5 = 5.274917218 n = 5.274917218 Simplifying n = 5.274917218Subproblem 2
n + -1.5 = -3.774917218 Simplifying n + -1.5 = -3.774917218 Reorder the terms: -1.5 + n = -3.774917218 Solving -1.5 + n = -3.774917218 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -3.774917218 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -3.774917218 + 1.5 n = -3.774917218 + 1.5 Combine like terms: -3.774917218 + 1.5 = -2.274917218 n = -2.274917218 Simplifying n = -2.274917218Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.274917218, -2.274917218}
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