n^2-6n-3=0

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Solution for n^2-6n-3=0 equation:


Simplifying
n2 + -6n + -3 = 0

Reorder the terms:
-3 + -6n + n2 = 0

Solving
-3 + -6n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -6n + 3 + n2 = 0 + 3

Reorder the terms:
-3 + 3 + -6n + n2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -6n + n2 = 0 + 3
-6n + n2 = 0 + 3

Combine like terms: 0 + 3 = 3
-6n + n2 = 3

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 = 3 + 9

Reorder the terms:
9 + -6n + n2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + -6n + n2 = 12

Factor a perfect square on the left side:
(n + -3)(n + -3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(n + -3) equal to 3.464101615 and -3.464101615.

Subproblem 1

n + -3 = 3.464101615 Simplifying n + -3 = 3.464101615 Reorder the terms: -3 + n = 3.464101615 Solving -3 + n = 3.464101615 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 = 3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + n = 3.464101615 + 3 n = 3.464101615 + 3 Combine like terms: 3.464101615 + 3 = 6.464101615 n = 6.464101615 Simplifying n = 6.464101615

Subproblem 2

n + -3 = -3.464101615 Simplifying n + -3 = -3.464101615 Reorder the terms: -3 + n = -3.464101615 Solving -3 + n = -3.464101615 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 = -3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + n = -3.464101615 + 3 n = -3.464101615 + 3 Combine like terms: -3.464101615 + 3 = -0.464101615 n = -0.464101615 Simplifying n = -0.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. n = {6.464101615, -0.464101615}

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