18x^2-3x-4=0

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Solution for 18x^2-3x-4=0 equation: 


Simplifying
18x2 + -3x + -4 = 0

Reorder the terms:
-4 + -3x + 18x2 = 0

Solving
-4 + -3x + 18x2 = 0

Solving for variable 'x'.

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

Divide each side by '18'.
-0.2222222222 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -0.1666666667x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -0.1666666667x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -0.1666666667x + x2 = 0 + 0.2222222222
-0.1666666667x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-0.1666666667x + x2 = 0.2222222222

The x term is -0.1666666667x.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667x + 0.006944444447 + x2 = 0.2222222222 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 0.2222222222 + 0.006944444447

Combine like terms: 0.2222222222 + 0.006944444447 = 0.229166666647
0.006944444447 + -0.1666666667x + x2 = 0.229166666647

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 0.229166666647

Calculate the square root of the right side: 0.478713554

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 0.478713554 and -0.478713554.


Subproblem 1
x + -0.08333333335 = 0.478713554

Simplifying
x + -0.08333333335 = 0.478713554

Reorder the terms:
-0.08333333335 + x = 0.478713554

Solving
-0.08333333335 + x = 0.478713554

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = 0.478713554 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = 0.478713554 + 0.08333333335
x = 0.478713554 + 0.08333333335

Combine like terms: 0.478713554 + 0.08333333335 = 0.56204688735
x = 0.56204688735

Simplifying
x = 0.56204688735


Subproblem 2
x + -0.08333333335 = -0.478713554

Simplifying
x + -0.08333333335 = -0.478713554

Reorder the terms:
-0.08333333335 + x = -0.478713554

Solving
-0.08333333335 + x = -0.478713554

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = -0.478713554 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = -0.478713554 + 0.08333333335
x = -0.478713554 + 0.08333333335

Combine like terms: -0.478713554 + 0.08333333335 = -0.39538022065
x = -0.39538022065

Simplifying
x = -0.39538022065


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.56204688735, -0.39538022065}

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