45x^2-144x+56=0

Solution for 45x^2-144x+56=0 equation:

Simplifying
45x2 + -144x + 56 = 0

Reorder the terms:
56 + -144x + 45x2 = 0

Solving
56 + -144x + 45x2 = 0

Solving for variable 'x'.

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

Divide each side by '45'.
1.244444444 + -3.2x + x2 = 0

Move the constant term to the right:

Add '-1.244444444' to each side of the equation.
1.244444444 + -3.2x + -1.244444444 + x2 = 0 + -1.244444444

Reorder the terms:
1.244444444 + -1.244444444 + -3.2x + x2 = 0 + -1.244444444

Combine like terms: 1.244444444 + -1.244444444 = 0.000000000
0.000000000 + -3.2x + x2 = 0 + -1.244444444
-3.2x + x2 = 0 + -1.244444444

Combine like terms: 0 + -1.244444444 = -1.244444444
-3.2x + x2 = -1.244444444

The x term is -3.2x.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2x + 2.56 + x2 = -1.244444444 + 2.56

Reorder the terms:
2.56 + -3.2x + x2 = -1.244444444 + 2.56

Combine like terms: -1.244444444 + 2.56 = 1.315555556
2.56 + -3.2x + x2 = 1.315555556

Factor a perfect square on the left side:
(x + -1.6)(x + -1.6) = 1.315555556

Calculate the square root of the right side: 1.146976702

Break this problem into two subproblems by setting 
(x + -1.6) equal to 1.146976702 and -1.146976702.

Subproblem 1
x + -1.6 = 1.146976702

Simplifying
x + -1.6 = 1.146976702

Reorder the terms:
-1.6 + x = 1.146976702

Solving
-1.6 + x = 1.146976702

Solving for variable 'x'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + x = 1.146976702 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + x = 1.146976702 + 1.6
x = 1.146976702 + 1.6

Combine like terms: 1.146976702 + 1.6 = 2.746976702
x = 2.746976702

Simplifying
x = 2.746976702

Subproblem 2
x + -1.6 = -1.146976702

Simplifying
x + -1.6 = -1.146976702

Reorder the terms:
-1.6 + x = -1.146976702

Solving
-1.6 + x = -1.146976702

Solving for variable 'x'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + x = -1.146976702 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + x = -1.146976702 + 1.6
x = -1.146976702 + 1.6

Combine like terms: -1.146976702 + 1.6 = 0.453023298
x = 0.453023298

Simplifying
x = 0.453023298

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.746976702, 0.453023298}