14x^2-45x+14=0

Solution for 14x^2-45x+14=0 equation:

Simplifying
14x2 + -45x + 14 = 0

Reorder the terms:
14 + -45x + 14x2 = 0

Solving
14 + -45x + 14x2 = 0

Solving for variable 'x'.

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

Divide each side by '14'.
1 + -3.214285714x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3.214285714x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -3.214285714x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3.214285714x + x2 = 0 + -1
-3.214285714x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3.214285714x + x2 = -1

The x term is -3.214285714x.  Take half its coefficient (-1.607142857).
Square it (2.582908163) and add it to both sides.

Add '2.582908163' to each side of the equation.
-3.214285714x + 2.582908163 + x2 = -1 + 2.582908163

Reorder the terms:
2.582908163 + -3.214285714x + x2 = -1 + 2.582908163

Combine like terms: -1 + 2.582908163 = 1.582908163
2.582908163 + -3.214285714x + x2 = 1.582908163

Factor a perfect square on the left side:
(x + -1.607142857)(x + -1.607142857) = 1.582908163

Calculate the square root of the right side: 1.258136782

Break this problem into two subproblems by setting 
(x + -1.607142857) equal to 1.258136782 and -1.258136782.

Subproblem 1
x + -1.607142857 = 1.258136782

Simplifying
x + -1.607142857 = 1.258136782

Reorder the terms:
-1.607142857 + x = 1.258136782

Solving
-1.607142857 + x = 1.258136782

Solving for variable 'x'.

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

Add '1.607142857' to each side of the equation.
-1.607142857 + 1.607142857 + x = 1.258136782 + 1.607142857

Combine like terms: -1.607142857 + 1.607142857 = 0.000000000
0.000000000 + x = 1.258136782 + 1.607142857
x = 1.258136782 + 1.607142857

Combine like terms: 1.258136782 + 1.607142857 = 2.865279639
x = 2.865279639

Simplifying
x = 2.865279639

Subproblem 2
x + -1.607142857 = -1.258136782

Simplifying
x + -1.607142857 = -1.258136782

Reorder the terms:
-1.607142857 + x = -1.258136782

Solving
-1.607142857 + x = -1.258136782

Solving for variable 'x'.

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

Add '1.607142857' to each side of the equation.
-1.607142857 + 1.607142857 + x = -1.258136782 + 1.607142857

Combine like terms: -1.607142857 + 1.607142857 = 0.000000000
0.000000000 + x = -1.258136782 + 1.607142857
x = -1.258136782 + 1.607142857

Combine like terms: -1.258136782 + 1.607142857 = 0.349006075
x = 0.349006075

Simplifying
x = 0.349006075

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.865279639, 0.349006075}