2x^2+4x-2.5=0

Solution for 2x^2+4x-2.5=0 equation:

Simplifying
2x2 + 4x + -2.5 = 0

Reorder the terms:
-2.5 + 4x + 2x2 = 0

Solving
-2.5 + 4x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-1.25 + 2x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 2x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 2x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 2x + x2 = 0 + 1.25
2x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
2x + x2 = 1.25

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 1.25 + 1

Reorder the terms:
1 + 2x + x2 = 1.25 + 1

Combine like terms: 1.25 + 1 = 2.25
1 + 2x + x2 = 2.25

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2.25

Calculate the square root of the right side: 1.5

Break this problem into two subproblems by setting 
(x + 1) equal to 1.5 and -1.5.

Subproblem 1
x + 1 = 1.5

Simplifying
x + 1 = 1.5

Reorder the terms:
1 + x = 1.5

Solving
1 + x = 1.5

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 1.5 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.5 + -1
x = 1.5 + -1

Combine like terms: 1.5 + -1 = 0.5
x = 0.5

Simplifying
x = 0.5

Subproblem 2
x + 1 = -1.5

Simplifying
x + 1 = -1.5

Reorder the terms:
1 + x = -1.5

Solving
1 + x = -1.5

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -1.5 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.5 + -1
x = -1.5 + -1

Combine like terms: -1.5 + -1 = -2.5
x = -2.5

Simplifying
x = -2.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -2.5}