4x^2+50x+34=0

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Solution for 4x^2+50x+34=0 equation: 


Simplifying
4x2 + 50x + 34 = 0

Reorder the terms:
34 + 50x + 4x2 = 0

Solving
34 + 50x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + 25x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(17 + 25x + 2x2)' equal to zero and attempt to solve:

Simplifying
17 + 25x + 2x2 = 0

Solving
17 + 25x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
8.5 + 12.5x + x2 = 0

Move the constant term to the right:

Add '-8.5' to each side of the equation.
8.5 + 12.5x + -8.5 + x2 = 0 + -8.5

Reorder the terms:
8.5 + -8.5 + 12.5x + x2 = 0 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + 12.5x + x2 = 0 + -8.5
12.5x + x2 = 0 + -8.5

Combine like terms: 0 + -8.5 = -8.5
12.5x + x2 = -8.5

The x term is 12.5x.  Take half its coefficient (6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
12.5x + 39.0625 + x2 = -8.5 + 39.0625

Reorder the terms:
39.0625 + 12.5x + x2 = -8.5 + 39.0625

Combine like terms: -8.5 + 39.0625 = 30.5625
39.0625 + 12.5x + x2 = 30.5625

Factor a perfect square on the left side:
(x + 6.25)(x + 6.25) = 30.5625

Calculate the square root of the right side: 5.528336097

Break this problem into two subproblems by setting 
(x + 6.25) equal to 5.528336097 and -5.528336097.


Subproblem 1
x + 6.25 = 5.528336097

Simplifying
x + 6.25 = 5.528336097

Reorder the terms:
6.25 + x = 5.528336097

Solving
6.25 + x = 5.528336097

Solving for variable 'x'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x = 5.528336097 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = 5.528336097 + -6.25
x = 5.528336097 + -6.25

Combine like terms: 5.528336097 + -6.25 = -0.721663903
x = -0.721663903

Simplifying
x = -0.721663903


Subproblem 2
x + 6.25 = -5.528336097

Simplifying
x + 6.25 = -5.528336097

Reorder the terms:
6.25 + x = -5.528336097

Solving
6.25 + x = -5.528336097

Solving for variable 'x'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x = -5.528336097 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = -5.528336097 + -6.25
x = -5.528336097 + -6.25

Combine like terms: -5.528336097 + -6.25 = -11.778336097
x = -11.778336097

Simplifying
x = -11.778336097


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.721663903, -11.778336097}
Solution
x = {-0.721663903, -11.778336097}

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