4x^2-x-0.5=0

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Solution for 4x^2-x-0.5=0 equation: 


Simplifying
4x2 + -1x + -0.5 = 0

Reorder the terms:
-0.5 + -1x + 4x2 = 0

Solving
-0.5 + -1x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-0.125 + -0.25x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -0.25x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -0.25x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -0.25x + x2 = 0 + 0.125
-0.25x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-0.25x + x2 = 0.125

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 0.125 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 0.125 + 0.015625

Combine like terms: 0.125 + 0.015625 = 0.140625
0.015625 + -0.25x + x2 = 0.140625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 0.140625

Calculate the square root of the right side: 0.375

Break this problem into two subproblems by setting 
(x + -0.125) equal to 0.375 and -0.375.


Subproblem 1
x + -0.125 = 0.375

Simplifying
x + -0.125 = 0.375

Reorder the terms:
-0.125 + x = 0.375

Solving
-0.125 + x = 0.375

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = 0.375 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 0.375 + 0.125
x = 0.375 + 0.125

Combine like terms: 0.375 + 0.125 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + -0.125 = -0.375

Simplifying
x + -0.125 = -0.375

Reorder the terms:
-0.125 + x = -0.375

Solving
-0.125 + x = -0.375

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = -0.375 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -0.375 + 0.125
x = -0.375 + 0.125

Combine like terms: -0.375 + 0.125 = -0.25
x = -0.25

Simplifying
x = -0.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -0.25}

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