2.5x(2.5x)+3x=2

Solution for 2.5x(2.5x)+3x=2 equation:

Simplifying
2.5x(2.5x) + 3x = 2

Remove parenthesis around (2.5x)
2.5x * 2.5x + 3x = 2

Reorder the terms for easier multiplication:
2.5 * 2.5x * x + 3x = 2

Multiply 2.5 * 2.5
6.25x * x + 3x = 2

Multiply x * x
6.25x2 + 3x = 2

Reorder the terms:
3x + 6.25x2 = 2

Solving
3x + 6.25x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + 3x + 6.25x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 3x + 6.25x2 = 0

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

Divide each side by '6.25'.
-0.32 + 0.48x + x2 = 0

Move the constant term to the right:

Add '0.32' to each side of the equation.
-0.32 + 0.48x + 0.32 + x2 = 0 + 0.32

Reorder the terms:
-0.32 + 0.32 + 0.48x + x2 = 0 + 0.32

Combine like terms: -0.32 + 0.32 = 0.00
0.00 + 0.48x + x2 = 0 + 0.32
0.48x + x2 = 0 + 0.32

Combine like terms: 0 + 0.32 = 0.32
0.48x + x2 = 0.32

The x term is 0.48x.  Take half its coefficient (0.24).
Square it (0.0576) and add it to both sides.

Add '0.0576' to each side of the equation.
0.48x + 0.0576 + x2 = 0.32 + 0.0576

Reorder the terms:
0.0576 + 0.48x + x2 = 0.32 + 0.0576

Combine like terms: 0.32 + 0.0576 = 0.3776
0.0576 + 0.48x + x2 = 0.3776

Factor a perfect square on the left side:
(x + 0.24)(x + 0.24) = 0.3776

Calculate the square root of the right side: 0.61449166

Break this problem into two subproblems by setting 
(x + 0.24) equal to 0.61449166 and -0.61449166.

Subproblem 1
x + 0.24 = 0.61449166

Simplifying
x + 0.24 = 0.61449166

Reorder the terms:
0.24 + x = 0.61449166

Solving
0.24 + x = 0.61449166

Solving for variable 'x'.

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

Add '-0.24' to each side of the equation.
0.24 + -0.24 + x = 0.61449166 + -0.24

Combine like terms: 0.24 + -0.24 = 0.00
0.00 + x = 0.61449166 + -0.24
x = 0.61449166 + -0.24

Combine like terms: 0.61449166 + -0.24 = 0.37449166
x = 0.37449166

Simplifying
x = 0.37449166

Subproblem 2
x + 0.24 = -0.61449166

Simplifying
x + 0.24 = -0.61449166

Reorder the terms:
0.24 + x = -0.61449166

Solving
0.24 + x = -0.61449166

Solving for variable 'x'.

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

Add '-0.24' to each side of the equation.
0.24 + -0.24 + x = -0.61449166 + -0.24

Combine like terms: 0.24 + -0.24 = 0.00
0.00 + x = -0.61449166 + -0.24
x = -0.61449166 + -0.24

Combine like terms: -0.61449166 + -0.24 = -0.85449166
x = -0.85449166

Simplifying
x = -0.85449166

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.37449166, -0.85449166}