4x^2-49x+9=0

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Solution for 4x^2-49x+9=0 equation: 


Simplifying
4x2 + -49x + 9 = 0

Reorder the terms:
9 + -49x + 4x2 = 0

Solving
9 + -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'.
2.25 + -12.25x + x2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -12.25x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -12.25x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -12.25x + x2 = 0 + -2.25
-12.25x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-12.25x + x2 = -2.25

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 = -2.25 + 37.515625

Reorder the terms:
37.515625 + -12.25x + x2 = -2.25 + 37.515625

Combine like terms: -2.25 + 37.515625 = 35.265625
37.515625 + -12.25x + x2 = 35.265625

Factor a perfect square on the left side:
(x + -6.125)(x + -6.125) = 35.265625

Calculate the square root of the right side: 5.93848676

Break this problem into two subproblems by setting 
(x + -6.125) equal to 5.93848676 and -5.93848676.


Subproblem 1
x + -6.125 = 5.93848676

Simplifying
x + -6.125 = 5.93848676

Reorder the terms:
-6.125 + x = 5.93848676

Solving
-6.125 + x = 5.93848676

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 = 5.93848676 + 6.125

Combine like terms: -6.125 + 6.125 = 0.000
0.000 + x = 5.93848676 + 6.125
x = 5.93848676 + 6.125

Combine like terms: 5.93848676 + 6.125 = 12.06348676
x = 12.06348676

Simplifying
x = 12.06348676


Subproblem 2
x + -6.125 = -5.93848676

Simplifying
x + -6.125 = -5.93848676

Reorder the terms:
-6.125 + x = -5.93848676

Solving
-6.125 + x = -5.93848676

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 = -5.93848676 + 6.125

Combine like terms: -6.125 + 6.125 = 0.000
0.000 + x = -5.93848676 + 6.125
x = -5.93848676 + 6.125

Combine like terms: -5.93848676 + 6.125 = 0.18651324
x = 0.18651324

Simplifying
x = 0.18651324


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.06348676, 0.18651324}

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