4x^2+33x+23=0

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Solution for 4x^2+33x+23=0 equation: 


Simplifying
4x2 + 33x + 23 = 0

Reorder the terms:
23 + 33x + 4x2 = 0

Solving
23 + 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'.
5.75 + 8.25x + x2 = 0

Move the constant term to the right:

Add '-5.75' to each side of the equation.
5.75 + 8.25x + -5.75 + x2 = 0 + -5.75

Reorder the terms:
5.75 + -5.75 + 8.25x + x2 = 0 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + 8.25x + x2 = 0 + -5.75
8.25x + x2 = 0 + -5.75

Combine like terms: 0 + -5.75 = -5.75
8.25x + x2 = -5.75

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 = -5.75 + 17.015625

Reorder the terms:
17.015625 + 8.25x + x2 = -5.75 + 17.015625

Combine like terms: -5.75 + 17.015625 = 11.265625
17.015625 + 8.25x + x2 = 11.265625

Factor a perfect square on the left side:
(x + 4.125)(x + 4.125) = 11.265625

Calculate the square root of the right side: 3.356430396

Break this problem into two subproblems by setting 
(x + 4.125) equal to 3.356430396 and -3.356430396.


Subproblem 1
x + 4.125 = 3.356430396

Simplifying
x + 4.125 = 3.356430396

Reorder the terms:
4.125 + x = 3.356430396

Solving
4.125 + x = 3.356430396

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 = 3.356430396 + -4.125

Combine like terms: 4.125 + -4.125 = 0.000
0.000 + x = 3.356430396 + -4.125
x = 3.356430396 + -4.125

Combine like terms: 3.356430396 + -4.125 = -0.768569604
x = -0.768569604

Simplifying
x = -0.768569604


Subproblem 2
x + 4.125 = -3.356430396

Simplifying
x + 4.125 = -3.356430396

Reorder the terms:
4.125 + x = -3.356430396

Solving
4.125 + x = -3.356430396

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 = -3.356430396 + -4.125

Combine like terms: 4.125 + -4.125 = 0.000
0.000 + x = -3.356430396 + -4.125
x = -3.356430396 + -4.125

Combine like terms: -3.356430396 + -4.125 = -7.481430396
x = -7.481430396

Simplifying
x = -7.481430396


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.768569604, -7.481430396}

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