25x^2-16x=5

Solution for 25x^2-16x=5 equation:

Simplifying
25x2 + -16x = 5

Reorder the terms:
-16x + 25x2 = 5

Solving
-16x + 25x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -16x + 25x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -16x + 25x2 = 0

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

Divide each side by '25'.
-0.2 + -0.64x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -0.64x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -0.64x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -0.64x + x2 = 0 + 0.2
-0.64x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-0.64x + x2 = 0.2

The x term is -0.64x.  Take half its coefficient (-0.32).
Square it (0.1024) and add it to both sides.

Add '0.1024' to each side of the equation.
-0.64x + 0.1024 + x2 = 0.2 + 0.1024

Reorder the terms:
0.1024 + -0.64x + x2 = 0.2 + 0.1024

Combine like terms: 0.2 + 0.1024 = 0.3024
0.1024 + -0.64x + x2 = 0.3024

Factor a perfect square on the left side:
(x + -0.32)(x + -0.32) = 0.3024

Calculate the square root of the right side: 0.549909083

Break this problem into two subproblems by setting 
(x + -0.32) equal to 0.549909083 and -0.549909083.

Subproblem 1
x + -0.32 = 0.549909083

Simplifying
x + -0.32 = 0.549909083

Reorder the terms:
-0.32 + x = 0.549909083

Solving
-0.32 + x = 0.549909083

Solving for variable 'x'.

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

Add '0.32' to each side of the equation.
-0.32 + 0.32 + x = 0.549909083 + 0.32

Combine like terms: -0.32 + 0.32 = 0.00
0.00 + x = 0.549909083 + 0.32
x = 0.549909083 + 0.32

Combine like terms: 0.549909083 + 0.32 = 0.869909083
x = 0.869909083

Simplifying
x = 0.869909083

Subproblem 2
x + -0.32 = -0.549909083

Simplifying
x + -0.32 = -0.549909083

Reorder the terms:
-0.32 + x = -0.549909083

Solving
-0.32 + x = -0.549909083

Solving for variable 'x'.

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

Add '0.32' to each side of the equation.
-0.32 + 0.32 + x = -0.549909083 + 0.32

Combine like terms: -0.32 + 0.32 = 0.00
0.00 + x = -0.549909083 + 0.32
x = -0.549909083 + 0.32

Combine like terms: -0.549909083 + 0.32 = -0.229909083
x = -0.229909083

Simplifying
x = -0.229909083

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.869909083, -0.229909083}