4x^2-49x-4=0

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Solution for 4x^2-49x-4=0 equation: 


Simplifying
4x2 + -49x + -4 = 0

Reorder the terms:
-4 + -49x + 4x2 = 0

Solving
-4 + -49x + 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'.
-1 + -12.25x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -12.25x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -12.25x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -12.25x + x2 = 0 + 1
-12.25x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-12.25x + x2 = 1

The x term is -12.25x.  Take half its coefficient (-6.125).
Square it (37.515625) and add it to both sides.

Add '37.515625' to each side of the equation.
-12.25x + 37.515625 + x2 = 1 + 37.515625

Reorder the terms:
37.515625 + -12.25x + x2 = 1 + 37.515625

Combine like terms: 1 + 37.515625 = 38.515625
37.515625 + -12.25x + x2 = 38.515625

Factor a perfect square on the left side:
(x + -6.125)(x + -6.125) = 38.515625

Calculate the square root of the right side: 6.206095794

Break this problem into two subproblems by setting 
(x + -6.125) equal to 6.206095794 and -6.206095794.


Subproblem 1
x + -6.125 = 6.206095794

Simplifying
x + -6.125 = 6.206095794

Reorder the terms:
-6.125 + x = 6.206095794

Solving
-6.125 + x = 6.206095794

Solving for variable 'x'.

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

Add '6.125' to each side of the equation.
-6.125 + 6.125 + x = 6.206095794 + 6.125

Combine like terms: -6.125 + 6.125 = 0.000
0.000 + x = 6.206095794 + 6.125
x = 6.206095794 + 6.125

Combine like terms: 6.206095794 + 6.125 = 12.331095794
x = 12.331095794

Simplifying
x = 12.331095794


Subproblem 2
x + -6.125 = -6.206095794

Simplifying
x + -6.125 = -6.206095794

Reorder the terms:
-6.125 + x = -6.206095794

Solving
-6.125 + x = -6.206095794

Solving for variable 'x'.

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

Add '6.125' to each side of the equation.
-6.125 + 6.125 + x = -6.206095794 + 6.125

Combine like terms: -6.125 + 6.125 = 0.000
0.000 + x = -6.206095794 + 6.125
x = -6.206095794 + 6.125

Combine like terms: -6.206095794 + 6.125 = -0.081095794
x = -0.081095794

Simplifying
x = -0.081095794


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.331095794, -0.081095794}

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