65.25x^2-26.28x=22645701.56

Solution for 65.25x^2-26.28x=22645701.56 equation:

Simplifying
65.25x2 + -26.28x = 22645701.56

Reorder the terms:
-26.28x + 65.25x2 = 22645701.56

Solving
-26.28x + 65.25x2 = 22645701.56

Solving for variable 'x'.

Reorder the terms:
-22645701.56 + -26.28x + 65.25x2 = 22645701.56 + -22645701.56

Combine like terms: 22645701.56 + -22645701.56 = 0.00
-22645701.56 + -26.28x + 65.25x2 = 0.00

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

Divide each side by '65.25'.
-347060.5603 + -0.4027586207x + x2 = 0

Move the constant term to the right:

Add '347060.5603' to each side of the equation.
-347060.5603 + -0.4027586207x + 347060.5603 + x2 = 0 + 347060.5603

Reorder the terms:
-347060.5603 + 347060.5603 + -0.4027586207x + x2 = 0 + 347060.5603

Combine like terms: -347060.5603 + 347060.5603 = 0.0000
0.0000 + -0.4027586207x + x2 = 0 + 347060.5603
-0.4027586207x + x2 = 0 + 347060.5603

Combine like terms: 0 + 347060.5603 = 347060.5603
-0.4027586207x + x2 = 347060.5603

The x term is -0.4027586207x.  Take half its coefficient (-0.2013793104).
Square it (0.04055362666) and add it to both sides.

Add '0.04055362666' to each side of the equation.
-0.4027586207x + 0.04055362666 + x2 = 347060.5603 + 0.04055362666

Reorder the terms:
0.04055362666 + -0.4027586207x + x2 = 347060.5603 + 0.04055362666

Combine like terms: 347060.5603 + 0.04055362666 = 347060.60085362666
0.04055362666 + -0.4027586207x + x2 = 347060.60085362666

Factor a perfect square on the left side:
(x + -0.2013793104)(x + -0.2013793104) = 347060.60085362666

Calculate the square root of the right side: 589.118494748

Break this problem into two subproblems by setting 
(x + -0.2013793104) equal to 589.118494748 and -589.118494748.

Subproblem 1
x + -0.2013793104 = 589.118494748

Simplifying
x + -0.2013793104 = 589.118494748

Reorder the terms:
-0.2013793104 + x = 589.118494748

Solving
-0.2013793104 + x = 589.118494748

Solving for variable 'x'.

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

Add '0.2013793104' to each side of the equation.
-0.2013793104 + 0.2013793104 + x = 589.118494748 + 0.2013793104

Combine like terms: -0.2013793104 + 0.2013793104 = 0.0000000000
0.0000000000 + x = 589.118494748 + 0.2013793104
x = 589.118494748 + 0.2013793104

Combine like terms: 589.118494748 + 0.2013793104 = 589.3198740584
x = 589.3198740584

Simplifying
x = 589.3198740584

Subproblem 2
x + -0.2013793104 = -589.118494748

Simplifying
x + -0.2013793104 = -589.118494748

Reorder the terms:
-0.2013793104 + x = -589.118494748

Solving
-0.2013793104 + x = -589.118494748

Solving for variable 'x'.

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

Add '0.2013793104' to each side of the equation.
-0.2013793104 + 0.2013793104 + x = -589.118494748 + 0.2013793104

Combine like terms: -0.2013793104 + 0.2013793104 = 0.0000000000
0.0000000000 + x = -589.118494748 + 0.2013793104
x = -589.118494748 + 0.2013793104

Combine like terms: -589.118494748 + 0.2013793104 = -588.9171154376
x = -588.9171154376

Simplifying
x = -588.9171154376

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {589.3198740584, -588.9171154376}