4x^2+33x+34=0

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Solution for 4x^2+33x+34=0 equation: 


Simplifying
4x2 + 33x + 34 = 0

Reorder the terms:
34 + 33x + 4x2 = 0

Solving
34 + 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'.
8.5 + 8.25x + x2 = 0

Move the constant term to the right:

Add '-8.5' to each side of the equation.
8.5 + 8.25x + -8.5 + x2 = 0 + -8.5

Reorder the terms:
8.5 + -8.5 + 8.25x + x2 = 0 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + 8.25x + x2 = 0 + -8.5
8.25x + x2 = 0 + -8.5

Combine like terms: 0 + -8.5 = -8.5
8.25x + x2 = -8.5

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 = -8.5 + 17.015625

Reorder the terms:
17.015625 + 8.25x + x2 = -8.5 + 17.015625

Combine like terms: -8.5 + 17.015625 = 8.515625
17.015625 + 8.25x + x2 = 8.515625

Factor a perfect square on the left side:
(x + 4.125)(x + 4.125) = 8.515625

Calculate the square root of the right side: 2.918154382

Break this problem into two subproblems by setting 
(x + 4.125) equal to 2.918154382 and -2.918154382.


Subproblem 1
x + 4.125 = 2.918154382

Simplifying
x + 4.125 = 2.918154382

Reorder the terms:
4.125 + x = 2.918154382

Solving
4.125 + x = 2.918154382

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 = 2.918154382 + -4.125

Combine like terms: 4.125 + -4.125 = 0.000
0.000 + x = 2.918154382 + -4.125
x = 2.918154382 + -4.125

Combine like terms: 2.918154382 + -4.125 = -1.206845618
x = -1.206845618

Simplifying
x = -1.206845618


Subproblem 2
x + 4.125 = -2.918154382

Simplifying
x + 4.125 = -2.918154382

Reorder the terms:
4.125 + x = -2.918154382

Solving
4.125 + x = -2.918154382

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 = -2.918154382 + -4.125

Combine like terms: 4.125 + -4.125 = 0.000
0.000 + x = -2.918154382 + -4.125
x = -2.918154382 + -4.125

Combine like terms: -2.918154382 + -4.125 = -7.043154382
x = -7.043154382

Simplifying
x = -7.043154382


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.206845618, -7.043154382}

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