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Simplifying -3n2 + 4n + -59 = -4n2 Reorder the terms: -59 + 4n + -3n2 = -4n2 Solving -59 + 4n + -3n2 = -4n2 Solving for variable 'n'. Combine like terms: -3n2 + 4n2 = 1n2 -59 + 4n + 1n2 = -4n2 + 4n2 Combine like terms: -4n2 + 4n2 = 0 -59 + 4n + 1n2 = 0 Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + 4n + 59 + n2 = 0 + 59 Reorder the terms: -59 + 59 + 4n + n2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + 4n + n2 = 0 + 59 4n + n2 = 0 + 59 Combine like terms: 0 + 59 = 59 4n + n2 = 59 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = 59 + 4 Reorder the terms: 4 + 4n + n2 = 59 + 4 Combine like terms: 59 + 4 = 63 4 + 4n + n2 = 63 Factor a perfect square on the left side: (n + 2)(n + 2) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (n + 2) equal to 7.937253933 and -7.937253933.Subproblem 1
n + 2 = 7.937253933 Simplifying n + 2 = 7.937253933 Reorder the terms: 2 + n = 7.937253933 Solving 2 + n = 7.937253933 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 7.937253933 + -2 Combine like terms: 2 + -2 = 0 0 + n = 7.937253933 + -2 n = 7.937253933 + -2 Combine like terms: 7.937253933 + -2 = 5.937253933 n = 5.937253933 Simplifying n = 5.937253933Subproblem 2
n + 2 = -7.937253933 Simplifying n + 2 = -7.937253933 Reorder the terms: 2 + n = -7.937253933 Solving 2 + n = -7.937253933 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -7.937253933 + -2 Combine like terms: 2 + -2 = 0 0 + n = -7.937253933 + -2 n = -7.937253933 + -2 Combine like terms: -7.937253933 + -2 = -9.937253933 n = -9.937253933 Simplifying n = -9.937253933Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.937253933, -9.937253933}
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