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Simplifying n2 + -6n + -51 = 3 Reorder the terms: -51 + -6n + n2 = 3 Solving -51 + -6n + n2 = 3 Solving for variable 'n'. Reorder the terms: -51 + -3 + -6n + n2 = 3 + -3 Combine like terms: -51 + -3 = -54 -54 + -6n + n2 = 3 + -3 Combine like terms: 3 + -3 = 0 -54 + -6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -6n + 54 + n2 = 0 + 54 Reorder the terms: -54 + 54 + -6n + n2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -6n + n2 = 0 + 54 -6n + n2 = 0 + 54 Combine like terms: 0 + 54 = 54 -6n + n2 = 54 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 = 54 + 9 Reorder the terms: 9 + -6n + n2 = 54 + 9 Combine like terms: 54 + 9 = 63 9 + -6n + n2 = 63 Factor a perfect square on the left side: (n + -3)(n + -3) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (n + -3) equal to 7.937253933 and -7.937253933.Subproblem 1
n + -3 = 7.937253933 Simplifying n + -3 = 7.937253933 Reorder the terms: -3 + n = 7.937253933 Solving -3 + n = 7.937253933 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 = 7.937253933 + 3 Combine like terms: -3 + 3 = 0 0 + n = 7.937253933 + 3 n = 7.937253933 + 3 Combine like terms: 7.937253933 + 3 = 10.937253933 n = 10.937253933 Simplifying n = 10.937253933Subproblem 2
n + -3 = -7.937253933 Simplifying n + -3 = -7.937253933 Reorder the terms: -3 + n = -7.937253933 Solving -3 + n = -7.937253933 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 = -7.937253933 + 3 Combine like terms: -3 + 3 = 0 0 + n = -7.937253933 + 3 n = -7.937253933 + 3 Combine like terms: -7.937253933 + 3 = -4.937253933 n = -4.937253933 Simplifying n = -4.937253933Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.937253933, -4.937253933}
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