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Simplifying n2 = -25 + -12n Solving n2 = -25 + -12n Solving for variable 'n'. Reorder the terms: 25 + 12n + n2 = -25 + -12n + 25 + 12n Reorder the terms: 25 + 12n + n2 = -25 + 25 + -12n + 12n Combine like terms: -25 + 25 = 0 25 + 12n + n2 = 0 + -12n + 12n 25 + 12n + n2 = -12n + 12n Combine like terms: -12n + 12n = 0 25 + 12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 12n + -25 + n2 = 0 + -25 Reorder the terms: 25 + -25 + 12n + n2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 12n + n2 = 0 + -25 12n + n2 = 0 + -25 Combine like terms: 0 + -25 = -25 12n + n2 = -25 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 = -25 + 36 Reorder the terms: 36 + 12n + n2 = -25 + 36 Combine like terms: -25 + 36 = 11 36 + 12n + n2 = 11 Factor a perfect square on the left side: (n + 6)(n + 6) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (n + 6) equal to 3.31662479 and -3.31662479.Subproblem 1
n + 6 = 3.31662479 Simplifying n + 6 = 3.31662479 Reorder the terms: 6 + n = 3.31662479 Solving 6 + n = 3.31662479 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 = 3.31662479 + -6 Combine like terms: 6 + -6 = 0 0 + n = 3.31662479 + -6 n = 3.31662479 + -6 Combine like terms: 3.31662479 + -6 = -2.68337521 n = -2.68337521 Simplifying n = -2.68337521Subproblem 2
n + 6 = -3.31662479 Simplifying n + 6 = -3.31662479 Reorder the terms: 6 + n = -3.31662479 Solving 6 + n = -3.31662479 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 = -3.31662479 + -6 Combine like terms: 6 + -6 = 0 0 + n = -3.31662479 + -6 n = -3.31662479 + -6 Combine like terms: -3.31662479 + -6 = -9.31662479 n = -9.31662479 Simplifying n = -9.31662479Solution
The solution to the problem is based on the solutions from the subproblems. n = {-2.68337521, -9.31662479}
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