28x^2-25x-1533=0

Solution for 28x^2-25x-1533=0 equation:

Simplifying
28x2 + -25x + -1533 = 0

Reorder the terms:
-1533 + -25x + 28x2 = 0

Solving
-1533 + -25x + 28x2 = 0

Solving for variable 'x'.

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

Divide each side by '28'.
-54.75 + -0.8928571429x + x2 = 0

Move the constant term to the right:

Add '54.75' to each side of the equation.
-54.75 + -0.8928571429x + 54.75 + x2 = 0 + 54.75

Reorder the terms:
-54.75 + 54.75 + -0.8928571429x + x2 = 0 + 54.75

Combine like terms: -54.75 + 54.75 = 0.00
0.00 + -0.8928571429x + x2 = 0 + 54.75
-0.8928571429x + x2 = 0 + 54.75

Combine like terms: 0 + 54.75 = 54.75
-0.8928571429x + x2 = 54.75

The x term is -0.8928571429x.  Take half its coefficient (-0.4464285715).
Square it (0.1992984695) and add it to both sides.

Add '0.1992984695' to each side of the equation.
-0.8928571429x + 0.1992984695 + x2 = 54.75 + 0.1992984695

Reorder the terms:
0.1992984695 + -0.8928571429x + x2 = 54.75 + 0.1992984695

Combine like terms: 54.75 + 0.1992984695 = 54.9492984695
0.1992984695 + -0.8928571429x + x2 = 54.9492984695

Factor a perfect square on the left side:
(x + -0.4464285715)(x + -0.4464285715) = 54.9492984695

Calculate the square root of the right side: 7.412779402

Break this problem into two subproblems by setting 
(x + -0.4464285715) equal to 7.412779402 and -7.412779402.

Subproblem 1
x + -0.4464285715 = 7.412779402

Simplifying
x + -0.4464285715 = 7.412779402

Reorder the terms:
-0.4464285715 + x = 7.412779402

Solving
-0.4464285715 + x = 7.412779402

Solving for variable 'x'.

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

Add '0.4464285715' to each side of the equation.
-0.4464285715 + 0.4464285715 + x = 7.412779402 + 0.4464285715

Combine like terms: -0.4464285715 + 0.4464285715 = 0.0000000000
0.0000000000 + x = 7.412779402 + 0.4464285715
x = 7.412779402 + 0.4464285715

Combine like terms: 7.412779402 + 0.4464285715 = 7.8592079735
x = 7.8592079735

Simplifying
x = 7.8592079735

Subproblem 2
x + -0.4464285715 = -7.412779402

Simplifying
x + -0.4464285715 = -7.412779402

Reorder the terms:
-0.4464285715 + x = -7.412779402

Solving
-0.4464285715 + x = -7.412779402

Solving for variable 'x'.

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

Add '0.4464285715' to each side of the equation.
-0.4464285715 + 0.4464285715 + x = -7.412779402 + 0.4464285715

Combine like terms: -0.4464285715 + 0.4464285715 = 0.0000000000
0.0000000000 + x = -7.412779402 + 0.4464285715
x = -7.412779402 + 0.4464285715

Combine like terms: -7.412779402 + 0.4464285715 = -6.9663508305
x = -6.9663508305

Simplifying
x = -6.9663508305

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.8592079735, -6.9663508305}