4x^2+1.6666x-1=0

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Solution for 4x^2+1.6666x-1=0 equation: 


Simplifying
4x2 + 1.6666x + -1 = 0

Reorder the terms:
-1 + 1.6666x + 4x2 = 0

Solving
-1 + 1.6666x + 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'.
-0.25 + 0.41665x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.41665x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.41665x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.41665x + x2 = 0 + 0.25
0.41665x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
0.41665x + x2 = 0.25

The x term is 0.41665x.  Take half its coefficient (0.208325).
Square it (0.04339930563) and add it to both sides.

Add '0.04339930563' to each side of the equation.
0.41665x + 0.04339930563 + x2 = 0.25 + 0.04339930563

Reorder the terms:
0.04339930563 + 0.41665x + x2 = 0.25 + 0.04339930563

Combine like terms: 0.25 + 0.04339930563 = 0.29339930563
0.04339930563 + 0.41665x + x2 = 0.29339930563

Factor a perfect square on the left side:
(x + 0.208325)(x + 0.208325) = 0.29339930563

Calculate the square root of the right side: 0.541663462

Break this problem into two subproblems by setting 
(x + 0.208325) equal to 0.541663462 and -0.541663462.


Subproblem 1
x + 0.208325 = 0.541663462

Simplifying
x + 0.208325 = 0.541663462

Reorder the terms:
0.208325 + x = 0.541663462

Solving
0.208325 + x = 0.541663462

Solving for variable 'x'.

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

Add '-0.208325' to each side of the equation.
0.208325 + -0.208325 + x = 0.541663462 + -0.208325

Combine like terms: 0.208325 + -0.208325 = 0.000000
0.000000 + x = 0.541663462 + -0.208325
x = 0.541663462 + -0.208325

Combine like terms: 0.541663462 + -0.208325 = 0.333338462
x = 0.333338462

Simplifying
x = 0.333338462


Subproblem 2
x + 0.208325 = -0.541663462

Simplifying
x + 0.208325 = -0.541663462

Reorder the terms:
0.208325 + x = -0.541663462

Solving
0.208325 + x = -0.541663462

Solving for variable 'x'.

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

Add '-0.208325' to each side of the equation.
0.208325 + -0.208325 + x = -0.541663462 + -0.208325

Combine like terms: 0.208325 + -0.208325 = 0.000000
0.000000 + x = -0.541663462 + -0.208325
x = -0.541663462 + -0.208325

Combine like terms: -0.541663462 + -0.208325 = -0.749988462
x = -0.749988462

Simplifying
x = -0.749988462


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.333338462, -0.749988462}

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