3x^2-25x+27=0

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Solution for 3x^2-25x+27=0 equation: 


Simplifying
3x2 + -25x + 27 = 0

Reorder the terms:
27 + -25x + 3x2 = 0

Solving
27 + -25x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
9 + -8.333333333x + x2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -8.333333333x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -8.333333333x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -8.333333333x + x2 = 0 + -9
-8.333333333x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-8.333333333x + x2 = -9

The x term is -8.333333333x.  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.
-8.333333333x + 17.36111111 + x2 = -9 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333x + x2 = -9 + 17.36111111

Combine like terms: -9 + 17.36111111 = 8.36111111
17.36111111 + -8.333333333x + x2 = 8.36111111

Factor a perfect square on the left side:
(x + -4.166666667)(x + -4.166666667) = 8.36111111

Calculate the square root of the right side: 2.891558595

Break this problem into two subproblems by setting 
(x + -4.166666667) equal to 2.891558595 and -2.891558595.


Subproblem 1
x + -4.166666667 = 2.891558595

Simplifying
x + -4.166666667 = 2.891558595

Reorder the terms:
-4.166666667 + x = 2.891558595

Solving
-4.166666667 + x = 2.891558595

Solving for variable 'x'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + x = 2.891558595 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = 2.891558595 + 4.166666667
x = 2.891558595 + 4.166666667

Combine like terms: 2.891558595 + 4.166666667 = 7.058225262
x = 7.058225262

Simplifying
x = 7.058225262


Subproblem 2
x + -4.166666667 = -2.891558595

Simplifying
x + -4.166666667 = -2.891558595

Reorder the terms:
-4.166666667 + x = -2.891558595

Solving
-4.166666667 + x = -2.891558595

Solving for variable 'x'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + x = -2.891558595 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = -2.891558595 + 4.166666667
x = -2.891558595 + 4.166666667

Combine like terms: -2.891558595 + 4.166666667 = 1.275108072
x = 1.275108072

Simplifying
x = 1.275108072


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.058225262, 1.275108072}

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