4x^2+33x+4=

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Solution for 4x^2+33x+4= equation: 


Simplifying
4x2 + 33x + 4 = 0

Reorder the terms:
4 + 33x + 4x2 = 0

Solving
4 + 33x + 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 + 8.25x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 8.25x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 8.25x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8.25x + x2 = 0 + -1
8.25x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
8.25x + x2 = -1

The x term is 8.25x.  Take half its coefficient (4.125).
Square it (17.015625) and add it to both sides.

Add '17.015625' to each side of the equation.
8.25x + 17.015625 + x2 = -1 + 17.015625

Reorder the terms:
17.015625 + 8.25x + x2 = -1 + 17.015625

Combine like terms: -1 + 17.015625 = 16.015625
17.015625 + 8.25x + x2 = 16.015625

Factor a perfect square on the left side:
(x + 4.125)(x + 4.125) = 16.015625

Calculate the square root of the right side: 4.001952648

Break this problem into two subproblems by setting 
(x + 4.125) equal to 4.001952648 and -4.001952648.


Subproblem 1
x + 4.125 = 4.001952648

Simplifying
x + 4.125 = 4.001952648

Reorder the terms:
4.125 + x = 4.001952648

Solving
4.125 + x = 4.001952648

Solving for variable 'x'.

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

Add '-4.125' to each side of the equation.
4.125 + -4.125 + x = 4.001952648 + -4.125

Combine like terms: 4.125 + -4.125 = 0.000
0.000 + x = 4.001952648 + -4.125
x = 4.001952648 + -4.125

Combine like terms: 4.001952648 + -4.125 = -0.123047352
x = -0.123047352

Simplifying
x = -0.123047352


Subproblem 2
x + 4.125 = -4.001952648

Simplifying
x + 4.125 = -4.001952648

Reorder the terms:
4.125 + x = -4.001952648

Solving
4.125 + x = -4.001952648

Solving for variable 'x'.

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

Add '-4.125' to each side of the equation.
4.125 + -4.125 + x = -4.001952648 + -4.125

Combine like terms: 4.125 + -4.125 = 0.000
0.000 + x = -4.001952648 + -4.125
x = -4.001952648 + -4.125

Combine like terms: -4.001952648 + -4.125 = -8.126952648
x = -8.126952648

Simplifying
x = -8.126952648


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.123047352, -8.126952648}

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