n^2-6n-46=0

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Solution for n^2-6n-46=0 equation:


Simplifying
n2 + -6n + -46 = 0

Reorder the terms:
-46 + -6n + n2 = 0

Solving
-46 + -6n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + -6n + 46 + n2 = 0 + 46

Reorder the terms:
-46 + 46 + -6n + n2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + -6n + n2 = 0 + 46
-6n + n2 = 0 + 46

Combine like terms: 0 + 46 = 46
-6n + n2 = 46

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 = 46 + 9

Reorder the terms:
9 + -6n + n2 = 46 + 9

Combine like terms: 46 + 9 = 55
9 + -6n + n2 = 55

Factor a perfect square on the left side:
(n + -3)(n + -3) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(n + -3) equal to 7.416198487 and -7.416198487.

Subproblem 1

n + -3 = 7.416198487 Simplifying n + -3 = 7.416198487 Reorder the terms: -3 + n = 7.416198487 Solving -3 + n = 7.416198487 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 = 7.416198487 + 3 Combine like terms: -3 + 3 = 0 0 + n = 7.416198487 + 3 n = 7.416198487 + 3 Combine like terms: 7.416198487 + 3 = 10.416198487 n = 10.416198487 Simplifying n = 10.416198487

Subproblem 2

n + -3 = -7.416198487 Simplifying n + -3 = -7.416198487 Reorder the terms: -3 + n = -7.416198487 Solving -3 + n = -7.416198487 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 = -7.416198487 + 3 Combine like terms: -3 + 3 = 0 0 + n = -7.416198487 + 3 n = -7.416198487 + 3 Combine like terms: -7.416198487 + 3 = -4.416198487 n = -4.416198487 Simplifying n = -4.416198487

Solution

The solution to the problem is based on the solutions from the subproblems. n = {10.416198487, -4.416198487}

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