.5x^2-2.5x-1.25=0

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Solution for .5x^2-2.5x-1.25=0 equation: 


Simplifying
0.5x2 + -2.5x + -1.25 = 0

Reorder the terms:
-1.25 + -2.5x + 0.5x2 = 0

Solving
-1.25 + -2.5x + 0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.5'.
-2.5 + -5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -5x + x2 = 0 + 2.5
-5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-5x + x2 = 2.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 2.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 2.5 + 6.25

Combine like terms: 2.5 + 6.25 = 8.75
6.25 + -5x + x2 = 8.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 8.75

Calculate the square root of the right side: 2.958039892

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.958039892 and -2.958039892.


Subproblem 1
x + -2.5 = 2.958039892

Simplifying
x + -2.5 = 2.958039892

Reorder the terms:
-2.5 + x = 2.958039892

Solving
-2.5 + x = 2.958039892

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.958039892 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.958039892 + 2.5
x = 2.958039892 + 2.5

Combine like terms: 2.958039892 + 2.5 = 5.458039892
x = 5.458039892

Simplifying
x = 5.458039892


Subproblem 2
x + -2.5 = -2.958039892

Simplifying
x + -2.5 = -2.958039892

Reorder the terms:
-2.5 + x = -2.958039892

Solving
-2.5 + x = -2.958039892

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.958039892 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.958039892 + 2.5
x = -2.958039892 + 2.5

Combine like terms: -2.958039892 + 2.5 = -0.458039892
x = -0.458039892

Simplifying
x = -0.458039892


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.458039892, -0.458039892}

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