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Simplifying 1n2 + -12n + -10 = 0 Reorder the terms: -10 + -12n + 1n2 = 0 Solving -10 + -12n + 1n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -12n + 10 + n2 = 0 + 10 Reorder the terms: -10 + 10 + -12n + n2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -12n + n2 = 0 + 10 -12n + n2 = 0 + 10 Combine like terms: 0 + 10 = 10 -12n + n2 = 10 The n term is -12n. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12n + 36 + n2 = 10 + 36 Reorder the terms: 36 + -12n + n2 = 10 + 36 Combine like terms: 10 + 36 = 46 36 + -12n + n2 = 46 Factor a perfect square on the left side: (n + -6)(n + -6) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (n + -6) equal to 6.782329983 and -6.782329983.Subproblem 1
n + -6 = 6.782329983 Simplifying n + -6 = 6.782329983 Reorder the terms: -6 + n = 6.782329983 Solving -6 + n = 6.782329983 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = 6.782329983 + 6 Combine like terms: -6 + 6 = 0 0 + n = 6.782329983 + 6 n = 6.782329983 + 6 Combine like terms: 6.782329983 + 6 = 12.782329983 n = 12.782329983 Simplifying n = 12.782329983Subproblem 2
n + -6 = -6.782329983 Simplifying n + -6 = -6.782329983 Reorder the terms: -6 + n = -6.782329983 Solving -6 + n = -6.782329983 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = -6.782329983 + 6 Combine like terms: -6 + 6 = 0 0 + n = -6.782329983 + 6 n = -6.782329983 + 6 Combine like terms: -6.782329983 + 6 = -0.782329983 n = -0.782329983 Simplifying n = -0.782329983Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.782329983, -0.782329983}
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