0.5x^2+0.875x-0.25=0

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Solution for 0.5x^2+0.875x-0.25=0 equation: 


Simplifying
0.5x2 + 0.875x + -0.25 = 0

Reorder the terms:
-0.25 + 0.875x + 0.5x2 = 0

Solving
-0.25 + 0.875x + 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'.
-0.5 + 1.75x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 1.75x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 1.75x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 1.75x + x2 = 0 + 0.5
1.75x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
1.75x + x2 = 0.5

The x term is 1.75x.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75x + 0.765625 + x2 = 0.5 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = 0.5 + 0.765625

Combine like terms: 0.5 + 0.765625 = 1.265625
0.765625 + 1.75x + x2 = 1.265625

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 1.265625

Calculate the square root of the right side: 1.125

Break this problem into two subproblems by setting 
(x + 0.875) equal to 1.125 and -1.125.


Subproblem 1
x + 0.875 = 1.125

Simplifying
x + 0.875 = 1.125

Reorder the terms:
0.875 + x = 1.125

Solving
0.875 + x = 1.125

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = 1.125 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = 1.125 + -0.875
x = 1.125 + -0.875

Combine like terms: 1.125 + -0.875 = 0.25
x = 0.25

Simplifying
x = 0.25


Subproblem 2
x + 0.875 = -1.125

Simplifying
x + 0.875 = -1.125

Reorder the terms:
0.875 + x = -1.125

Solving
0.875 + x = -1.125

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = -1.125 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = -1.125 + -0.875
x = -1.125 + -0.875

Combine like terms: -1.125 + -0.875 = -2
x = -2

Simplifying
x = -2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.25, -2}

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