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Simplifying n2 + -3 = 14n Reorder the terms: -3 + n2 = 14n Solving -3 + n2 = 14n Solving for variable 'n'. Reorder the terms: -3 + -14n + n2 = 14n + -14n Combine like terms: 14n + -14n = 0 -3 + -14n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -14n + 3 + n2 = 0 + 3 Reorder the terms: -3 + 3 + -14n + n2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -14n + n2 = 0 + 3 -14n + n2 = 0 + 3 Combine like terms: 0 + 3 = 3 -14n + n2 = 3 The n term is -14n. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14n + 49 + n2 = 3 + 49 Reorder the terms: 49 + -14n + n2 = 3 + 49 Combine like terms: 3 + 49 = 52 49 + -14n + n2 = 52 Factor a perfect square on the left side: (n + -7)(n + -7) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (n + -7) equal to 7.211102551 and -7.211102551.Subproblem 1
n + -7 = 7.211102551 Simplifying n + -7 = 7.211102551 Reorder the terms: -7 + n = 7.211102551 Solving -7 + n = 7.211102551 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = 7.211102551 + 7 Combine like terms: -7 + 7 = 0 0 + n = 7.211102551 + 7 n = 7.211102551 + 7 Combine like terms: 7.211102551 + 7 = 14.211102551 n = 14.211102551 Simplifying n = 14.211102551Subproblem 2
n + -7 = -7.211102551 Simplifying n + -7 = -7.211102551 Reorder the terms: -7 + n = -7.211102551 Solving -7 + n = -7.211102551 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = -7.211102551 + 7 Combine like terms: -7 + 7 = 0 0 + n = -7.211102551 + 7 n = -7.211102551 + 7 Combine like terms: -7.211102551 + 7 = -0.211102551 n = -0.211102551 Simplifying n = -0.211102551Solution
The solution to the problem is based on the solutions from the subproblems. n = {14.211102551, -0.211102551}
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