3n^2-25n+24=0

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Solution for 3n^2-25n+24=0 equation: 


Simplifying
3n2 + -25n + 24 = 0

Reorder the terms:
24 + -25n + 3n2 = 0

Solving
24 + -25n + 3n2 = 0

Solving for variable 'n'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
8 + -8.333333333n + n2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -8.333333333n + -8 + n2 = 0 + -8

Reorder the terms:
8 + -8 + -8.333333333n + n2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -8.333333333n + n2 = 0 + -8
-8.333333333n + n2 = 0 + -8

Combine like terms: 0 + -8 = -8
-8.333333333n + n2 = -8

The n term is -8.333333333n.  Take half its coefficient (-4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
-8.333333333n + 17.36111111 + n2 = -8 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333n + n2 = -8 + 17.36111111

Combine like terms: -8 + 17.36111111 = 9.36111111
17.36111111 + -8.333333333n + n2 = 9.36111111

Factor a perfect square on the left side:
(n + -4.166666667)(n + -4.166666667) = 9.36111111

Calculate the square root of the right side: 3.059593292

Break this problem into two subproblems by setting 
(n + -4.166666667) equal to 3.059593292 and -3.059593292.


Subproblem 1
n + -4.166666667 = 3.059593292

Simplifying
n + -4.166666667 = 3.059593292

Reorder the terms:
-4.166666667 + n = 3.059593292

Solving
-4.166666667 + n = 3.059593292

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + n = 3.059593292 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + n = 3.059593292 + 4.166666667
n = 3.059593292 + 4.166666667

Combine like terms: 3.059593292 + 4.166666667 = 7.226259959
n = 7.226259959

Simplifying
n = 7.226259959


Subproblem 2
n + -4.166666667 = -3.059593292

Simplifying
n + -4.166666667 = -3.059593292

Reorder the terms:
-4.166666667 + n = -3.059593292

Solving
-4.166666667 + n = -3.059593292

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + n = -3.059593292 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + n = -3.059593292 + 4.166666667
n = -3.059593292 + 4.166666667

Combine like terms: -3.059593292 + 4.166666667 = 1.107073375
n = 1.107073375

Simplifying
n = 1.107073375


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.226259959, 1.107073375}

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