0.25x^2+3x-7=0

Solution for 0.25x^2+3x-7=0 equation:

Simplifying
0.25x2 + 3x + -7 = 0

Reorder the terms:
-7 + 3x + 0.25x2 = 0

Solving
-7 + 3x + 0.25x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.25'.
-28 + 12x + x2 = 0

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 12x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 12x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 12x + x2 = 0 + 28
12x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
12x + x2 = 28

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 28 + 36

Reorder the terms:
36 + 12x + x2 = 28 + 36

Combine like terms: 28 + 36 = 64
36 + 12x + x2 = 64

Factor a perfect square on the left side:
(x + 6)(x + 6) = 64

Calculate the square root of the right side: 8

Break this problem into two subproblems by setting 
(x + 6) equal to 8 and -8.

Subproblem 1
x + 6 = 8

Simplifying
x + 6 = 8

Reorder the terms:
6 + x = 8

Solving
6 + x = 8

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 8 + -6

Combine like terms: 6 + -6 = 0
0 + x = 8 + -6
x = 8 + -6

Combine like terms: 8 + -6 = 2
x = 2

Simplifying
x = 2

Subproblem 2
x + 6 = -8

Simplifying
x + 6 = -8

Reorder the terms:
6 + x = -8

Solving
6 + x = -8

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -8 + -6

Combine like terms: 6 + -6 = 0
0 + x = -8 + -6
x = -8 + -6

Combine like terms: -8 + -6 = -14
x = -14

Simplifying
x = -14

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2, -14}