4x^2+2x-0.5=0

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


Simplifying
4x2 + 2x + -0.5 = 0

Reorder the terms:
-0.5 + 2x + 4x2 = 0

Solving
-0.5 + 2x + 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 + 0.5x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 0.5x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 0.5x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 0.5x + x2 = 0 + 0.125
0.5x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
0.5x + x2 = 0.125

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 0.125 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 0.125 + 0.0625

Combine like terms: 0.125 + 0.0625 = 0.1875
0.0625 + 0.5x + x2 = 0.1875

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.1875

Calculate the square root of the right side: 0.433012702

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.433012702 and -0.433012702.


Subproblem 1
x + 0.25 = 0.433012702

Simplifying
x + 0.25 = 0.433012702

Reorder the terms:
0.25 + x = 0.433012702

Solving
0.25 + x = 0.433012702

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.433012702 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.433012702 + -0.25
x = 0.433012702 + -0.25

Combine like terms: 0.433012702 + -0.25 = 0.183012702
x = 0.183012702

Simplifying
x = 0.183012702


Subproblem 2
x + 0.25 = -0.433012702

Simplifying
x + 0.25 = -0.433012702

Reorder the terms:
0.25 + x = -0.433012702

Solving
0.25 + x = -0.433012702

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.433012702 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.433012702 + -0.25
x = -0.433012702 + -0.25

Combine like terms: -0.433012702 + -0.25 = -0.683012702
x = -0.683012702

Simplifying
x = -0.683012702


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.183012702, -0.683012702}

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