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Simplifying n2 + -6n + -1 = 25 Reorder the terms: -1 + -6n + n2 = 25 Solving -1 + -6n + n2 = 25 Solving for variable 'n'. Reorder the terms: -1 + -25 + -6n + n2 = 25 + -25 Combine like terms: -1 + -25 = -26 -26 + -6n + n2 = 25 + -25 Combine like terms: 25 + -25 = 0 -26 + -6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -6n + 26 + n2 = 0 + 26 Reorder the terms: -26 + 26 + -6n + n2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -6n + n2 = 0 + 26 -6n + n2 = 0 + 26 Combine like terms: 0 + 26 = 26 -6n + n2 = 26 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 = 26 + 9 Reorder the terms: 9 + -6n + n2 = 26 + 9 Combine like terms: 26 + 9 = 35 9 + -6n + n2 = 35 Factor a perfect square on the left side: (n + -3)(n + -3) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (n + -3) equal to 5.916079783 and -5.916079783.Subproblem 1
n + -3 = 5.916079783 Simplifying n + -3 = 5.916079783 Reorder the terms: -3 + n = 5.916079783 Solving -3 + n = 5.916079783 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 = 5.916079783 + 3 Combine like terms: -3 + 3 = 0 0 + n = 5.916079783 + 3 n = 5.916079783 + 3 Combine like terms: 5.916079783 + 3 = 8.916079783 n = 8.916079783 Simplifying n = 8.916079783Subproblem 2
n + -3 = -5.916079783 Simplifying n + -3 = -5.916079783 Reorder the terms: -3 + n = -5.916079783 Solving -3 + n = -5.916079783 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 = -5.916079783 + 3 Combine like terms: -3 + 3 = 0 0 + n = -5.916079783 + 3 n = -5.916079783 + 3 Combine like terms: -5.916079783 + 3 = -2.916079783 n = -2.916079783 Simplifying n = -2.916079783Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.916079783, -2.916079783}
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