8x^2-3x-4=0

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Solution for 8x^2-3x-4=0 equation: 


Simplifying
8x2 + -3x + -4 = 0

Reorder the terms:
-4 + -3x + 8x2 = 0

Solving
-4 + -3x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-0.5 + -0.375x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.375x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.375x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.375x + x2 = 0 + 0.5
-0.375x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.375x + x2 = 0.5

The x term is -0.375x.  Take half its coefficient (-0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
-0.375x + 0.03515625 + x2 = 0.5 + 0.03515625

Reorder the terms:
0.03515625 + -0.375x + x2 = 0.5 + 0.03515625

Combine like terms: 0.5 + 0.03515625 = 0.53515625
0.03515625 + -0.375x + x2 = 0.53515625

Factor a perfect square on the left side:
(x + -0.1875)(x + -0.1875) = 0.53515625

Calculate the square root of the right side: 0.731543744

Break this problem into two subproblems by setting 
(x + -0.1875) equal to 0.731543744 and -0.731543744.


Subproblem 1
x + -0.1875 = 0.731543744

Simplifying
x + -0.1875 = 0.731543744

Reorder the terms:
-0.1875 + x = 0.731543744

Solving
-0.1875 + x = 0.731543744

Solving for variable 'x'.

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

Add '0.1875' to each side of the equation.
-0.1875 + 0.1875 + x = 0.731543744 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + x = 0.731543744 + 0.1875
x = 0.731543744 + 0.1875

Combine like terms: 0.731543744 + 0.1875 = 0.919043744
x = 0.919043744

Simplifying
x = 0.919043744


Subproblem 2
x + -0.1875 = -0.731543744

Simplifying
x + -0.1875 = -0.731543744

Reorder the terms:
-0.1875 + x = -0.731543744

Solving
-0.1875 + x = -0.731543744

Solving for variable 'x'.

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

Add '0.1875' to each side of the equation.
-0.1875 + 0.1875 + x = -0.731543744 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + x = -0.731543744 + 0.1875
x = -0.731543744 + 0.1875

Combine like terms: -0.731543744 + 0.1875 = -0.544043744
x = -0.544043744

Simplifying
x = -0.544043744


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.919043744, -0.544043744}

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