.25x^2+.5x=.75

Solution for .25x^2+.5x=.75 equation:

Simplifying
0.25x2 + 0.5x = 0.75

Reorder the terms:
0.5x + 0.25x2 = 0.75

Solving
0.5x + 0.25x2 = 0.75

Solving for variable 'x'.

Reorder the terms:
-0.75 + 0.5x + 0.25x2 = 0.75 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
-0.75 + 0.5x + 0.25x2 = 0.00

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

Divide each side by '0.25'.
-3 + 2x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 2x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 2x + x2 = 0 + 3

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

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

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 = 3 + 1

Reorder the terms:
1 + 2x + x2 = 3 + 1

Combine like terms: 3 + 1 = 4
1 + 2x + x2 = 4

Factor a perfect square on the left side:
(x + 1)(x + 1) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + 1) equal to 2 and -2.

Subproblem 1
x + 1 = 2

Simplifying
x + 1 = 2

Reorder the terms:
1 + x = 2

Solving
1 + x = 2

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 = 2 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2 + -1
x = 2 + -1

Combine like terms: 2 + -1 = 1
x = 1

Simplifying
x = 1

Subproblem 2
x + 1 = -2

Simplifying
x + 1 = -2

Reorder the terms:
1 + x = -2

Solving
1 + x = -2

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 = -2 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2 + -1
x = -2 + -1

Combine like terms: -2 + -1 = -3
x = -3

Simplifying
x = -3

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1, -3}