2x^2-27x+16=0

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Solution for 2x^2-27x+16=0 equation: 


Simplifying
2x2 + -27x + 16 = 0

Reorder the terms:
16 + -27x + 2x2 = 0

Solving
16 + -27x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
8 + -13.5x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -13.5x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -13.5x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -13.5x + x2 = 0 + -8
-13.5x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-13.5x + x2 = -8

The x term is -13.5x.  Take half its coefficient (-6.75).
Square it (45.5625) and add it to both sides.

Add '45.5625' to each side of the equation.
-13.5x + 45.5625 + x2 = -8 + 45.5625

Reorder the terms:
45.5625 + -13.5x + x2 = -8 + 45.5625

Combine like terms: -8 + 45.5625 = 37.5625
45.5625 + -13.5x + x2 = 37.5625

Factor a perfect square on the left side:
(x + -6.75)(x + -6.75) = 37.5625

Calculate the square root of the right side: 6.128825336

Break this problem into two subproblems by setting 
(x + -6.75) equal to 6.128825336 and -6.128825336.


Subproblem 1
x + -6.75 = 6.128825336

Simplifying
x + -6.75 = 6.128825336

Reorder the terms:
-6.75 + x = 6.128825336

Solving
-6.75 + x = 6.128825336

Solving for variable 'x'.

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

Add '6.75' to each side of the equation.
-6.75 + 6.75 + x = 6.128825336 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + x = 6.128825336 + 6.75
x = 6.128825336 + 6.75

Combine like terms: 6.128825336 + 6.75 = 12.878825336
x = 12.878825336

Simplifying
x = 12.878825336


Subproblem 2
x + -6.75 = -6.128825336

Simplifying
x + -6.75 = -6.128825336

Reorder the terms:
-6.75 + x = -6.128825336

Solving
-6.75 + x = -6.128825336

Solving for variable 'x'.

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

Add '6.75' to each side of the equation.
-6.75 + 6.75 + x = -6.128825336 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + x = -6.128825336 + 6.75
x = -6.128825336 + 6.75

Combine like terms: -6.128825336 + 6.75 = 0.621174664
x = 0.621174664

Simplifying
x = 0.621174664


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.878825336, 0.621174664}

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