275.625x^2-600x+290.625=0

Solution for 275.625x^2-600x+290.625=0 equation:

Simplifying
275.625x2 + -600x + 290.625 = 0

Reorder the terms:
290.625 + -600x + 275.625x2 = 0

Solving
290.625 + -600x + 275.625x2 = 0

Solving for variable 'x'.

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

Divide each side by '275.625'.
1.054421769 + -2.176870748x + x2 = 0

Move the constant term to the right:

Add '-1.054421769' to each side of the equation.
1.054421769 + -2.176870748x + -1.054421769 + x2 = 0 + -1.054421769

Reorder the terms:
1.054421769 + -1.054421769 + -2.176870748x + x2 = 0 + -1.054421769

Combine like terms: 1.054421769 + -1.054421769 = 0.000000000
0.000000000 + -2.176870748x + x2 = 0 + -1.054421769
-2.176870748x + x2 = 0 + -1.054421769

Combine like terms: 0 + -1.054421769 = -1.054421769
-2.176870748x + x2 = -1.054421769

The x term is -2.176870748x.  Take half its coefficient (-1.088435374).
Square it (1.184691563) and add it to both sides.

Add '1.184691563' to each side of the equation.
-2.176870748x + 1.184691563 + x2 = -1.054421769 + 1.184691563

Reorder the terms:
1.184691563 + -2.176870748x + x2 = -1.054421769 + 1.184691563

Combine like terms: -1.054421769 + 1.184691563 = 0.130269794
1.184691563 + -2.176870748x + x2 = 0.130269794

Factor a perfect square on the left side:
(x + -1.088435374)(x + -1.088435374) = 0.130269794

Calculate the square root of the right side: 0.360929071

Break this problem into two subproblems by setting 
(x + -1.088435374) equal to 0.360929071 and -0.360929071.

Subproblem 1
x + -1.088435374 = 0.360929071

Simplifying
x + -1.088435374 = 0.360929071

Reorder the terms:
-1.088435374 + x = 0.360929071

Solving
-1.088435374 + x = 0.360929071

Solving for variable 'x'.

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

Add '1.088435374' to each side of the equation.
-1.088435374 + 1.088435374 + x = 0.360929071 + 1.088435374

Combine like terms: -1.088435374 + 1.088435374 = 0.000000000
0.000000000 + x = 0.360929071 + 1.088435374
x = 0.360929071 + 1.088435374

Combine like terms: 0.360929071 + 1.088435374 = 1.449364445
x = 1.449364445

Simplifying
x = 1.449364445

Subproblem 2
x + -1.088435374 = -0.360929071

Simplifying
x + -1.088435374 = -0.360929071

Reorder the terms:
-1.088435374 + x = -0.360929071

Solving
-1.088435374 + x = -0.360929071

Solving for variable 'x'.

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

Add '1.088435374' to each side of the equation.
-1.088435374 + 1.088435374 + x = -0.360929071 + 1.088435374

Combine like terms: -1.088435374 + 1.088435374 = 0.000000000
0.000000000 + x = -0.360929071 + 1.088435374
x = -0.360929071 + 1.088435374

Combine like terms: -0.360929071 + 1.088435374 = 0.727506303
x = 0.727506303

Simplifying
x = 0.727506303

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.449364445, 0.727506303}