23x^2-57x+27=0

Solution for 23x^2-57x+27=0 equation:

Simplifying
23x2 + -57x + 27 = 0

Reorder the terms:
27 + -57x + 23x2 = 0

Solving
27 + -57x + 23x2 = 0

Solving for variable 'x'.

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

Divide each side by '23'.
1.173913043 + -2.47826087x + x2 = 0

Move the constant term to the right:

Add '-1.173913043' to each side of the equation.
1.173913043 + -2.47826087x + -1.173913043 + x2 = 0 + -1.173913043

Reorder the terms:
1.173913043 + -1.173913043 + -2.47826087x + x2 = 0 + -1.173913043

Combine like terms: 1.173913043 + -1.173913043 = 0.000000000
0.000000000 + -2.47826087x + x2 = 0 + -1.173913043
-2.47826087x + x2 = 0 + -1.173913043

Combine like terms: 0 + -1.173913043 = -1.173913043
-2.47826087x + x2 = -1.173913043

The x term is -2.47826087x.  Take half its coefficient (-1.239130435).
Square it (1.535444235) and add it to both sides.

Add '1.535444235' to each side of the equation.
-2.47826087x + 1.535444235 + x2 = -1.173913043 + 1.535444235

Reorder the terms:
1.535444235 + -2.47826087x + x2 = -1.173913043 + 1.535444235

Combine like terms: -1.173913043 + 1.535444235 = 0.361531192
1.535444235 + -2.47826087x + x2 = 0.361531192

Factor a perfect square on the left side:
(x + -1.239130435)(x + -1.239130435) = 0.361531192

Calculate the square root of the right side: 0.601274639

Break this problem into two subproblems by setting 
(x + -1.239130435) equal to 0.601274639 and -0.601274639.

Subproblem 1
x + -1.239130435 = 0.601274639

Simplifying
x + -1.239130435 = 0.601274639

Reorder the terms:
-1.239130435 + x = 0.601274639

Solving
-1.239130435 + x = 0.601274639

Solving for variable 'x'.

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

Add '1.239130435' to each side of the equation.
-1.239130435 + 1.239130435 + x = 0.601274639 + 1.239130435

Combine like terms: -1.239130435 + 1.239130435 = 0.000000000
0.000000000 + x = 0.601274639 + 1.239130435
x = 0.601274639 + 1.239130435

Combine like terms: 0.601274639 + 1.239130435 = 1.840405074
x = 1.840405074

Simplifying
x = 1.840405074

Subproblem 2
x + -1.239130435 = -0.601274639

Simplifying
x + -1.239130435 = -0.601274639

Reorder the terms:
-1.239130435 + x = -0.601274639

Solving
-1.239130435 + x = -0.601274639

Solving for variable 'x'.

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

Add '1.239130435' to each side of the equation.
-1.239130435 + 1.239130435 + x = -0.601274639 + 1.239130435

Combine like terms: -1.239130435 + 1.239130435 = 0.000000000
0.000000000 + x = -0.601274639 + 1.239130435
x = -0.601274639 + 1.239130435

Combine like terms: -0.601274639 + 1.239130435 = 0.637855796
x = 0.637855796

Simplifying
x = 0.637855796

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.840405074, 0.637855796}