14x^2-51x+45=5x^2-2x+1

Solution for 14x^2-51x+45=5x^2-2x+1 equation:

Simplifying
14x2 + -51x + 45 = 5x2 + -2x + 1

Reorder the terms:
45 + -51x + 14x2 = 5x2 + -2x + 1

Reorder the terms:
45 + -51x + 14x2 = 1 + -2x + 5x2

Solving
45 + -51x + 14x2 = 1 + -2x + 5x2

Solving for variable 'x'.

Reorder the terms:
45 + -1 + -51x + 2x + 14x2 + -5x2 = 1 + -2x + 5x2 + -1 + 2x + -5x2

Combine like terms: 45 + -1 = 44
44 + -51x + 2x + 14x2 + -5x2 = 1 + -2x + 5x2 + -1 + 2x + -5x2

Combine like terms: -51x + 2x = -49x
44 + -49x + 14x2 + -5x2 = 1 + -2x + 5x2 + -1 + 2x + -5x2

Combine like terms: 14x2 + -5x2 = 9x2
44 + -49x + 9x2 = 1 + -2x + 5x2 + -1 + 2x + -5x2

Reorder the terms:
44 + -49x + 9x2 = 1 + -1 + -2x + 2x + 5x2 + -5x2

Combine like terms: 1 + -1 = 0
44 + -49x + 9x2 = 0 + -2x + 2x + 5x2 + -5x2
44 + -49x + 9x2 = -2x + 2x + 5x2 + -5x2

Combine like terms: -2x + 2x = 0
44 + -49x + 9x2 = 0 + 5x2 + -5x2
44 + -49x + 9x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
44 + -49x + 9x2 = 0

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

Divide each side by '9'.
4.888888889 + -5.444444444x + x2 = 0

Move the constant term to the right:

Add '-4.888888889' to each side of the equation.
4.888888889 + -5.444444444x + -4.888888889 + x2 = 0 + -4.888888889

Reorder the terms:
4.888888889 + -4.888888889 + -5.444444444x + x2 = 0 + -4.888888889

Combine like terms: 4.888888889 + -4.888888889 = 0.000000000
0.000000000 + -5.444444444x + x2 = 0 + -4.888888889
-5.444444444x + x2 = 0 + -4.888888889

Combine like terms: 0 + -4.888888889 = -4.888888889
-5.444444444x + x2 = -4.888888889

The x term is -5.444444444x.  Take half its coefficient (-2.722222222).
Square it (7.410493826) and add it to both sides.

Add '7.410493826' to each side of the equation.
-5.444444444x + 7.410493826 + x2 = -4.888888889 + 7.410493826

Reorder the terms:
7.410493826 + -5.444444444x + x2 = -4.888888889 + 7.410493826

Combine like terms: -4.888888889 + 7.410493826 = 2.521604937
7.410493826 + -5.444444444x + x2 = 2.521604937

Factor a perfect square on the left side:
(x + -2.722222222)(x + -2.722222222) = 2.521604937

Calculate the square root of the right side: 1.587956214

Break this problem into two subproblems by setting 
(x + -2.722222222) equal to 1.587956214 and -1.587956214.

Subproblem 1
x + -2.722222222 = 1.587956214

Simplifying
x + -2.722222222 = 1.587956214

Reorder the terms:
-2.722222222 + x = 1.587956214

Solving
-2.722222222 + x = 1.587956214

Solving for variable 'x'.

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

Add '2.722222222' to each side of the equation.
-2.722222222 + 2.722222222 + x = 1.587956214 + 2.722222222

Combine like terms: -2.722222222 + 2.722222222 = 0.000000000
0.000000000 + x = 1.587956214 + 2.722222222
x = 1.587956214 + 2.722222222

Combine like terms: 1.587956214 + 2.722222222 = 4.310178436
x = 4.310178436

Simplifying
x = 4.310178436

Subproblem 2
x + -2.722222222 = -1.587956214

Simplifying
x + -2.722222222 = -1.587956214

Reorder the terms:
-2.722222222 + x = -1.587956214

Solving
-2.722222222 + x = -1.587956214

Solving for variable 'x'.

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

Add '2.722222222' to each side of the equation.
-2.722222222 + 2.722222222 + x = -1.587956214 + 2.722222222

Combine like terms: -2.722222222 + 2.722222222 = 0.000000000
0.000000000 + x = -1.587956214 + 2.722222222
x = -1.587956214 + 2.722222222

Combine like terms: -1.587956214 + 2.722222222 = 1.134266008
x = 1.134266008

Simplifying
x = 1.134266008

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.310178436, 1.134266008}