4x^2+118x+50=0

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Solution for 4x^2+118x+50=0 equation: 


Simplifying
4x2 + 118x + 50 = 0

Reorder the terms:
50 + 118x + 4x2 = 0

Solving
50 + 118x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 59x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + 59x + 2x2)' equal to zero and attempt to solve:

Simplifying
25 + 59x + 2x2 = 0

Solving
25 + 59x + 2x2 = 0

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

Divide each side by '2'.
12.5 + 29.5x + x2 = 0

Move the constant term to the right:

Add '-12.5' to each side of the equation.
12.5 + 29.5x + -12.5 + x2 = 0 + -12.5

Reorder the terms:
12.5 + -12.5 + 29.5x + x2 = 0 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + 29.5x + x2 = 0 + -12.5
29.5x + x2 = 0 + -12.5

Combine like terms: 0 + -12.5 = -12.5
29.5x + x2 = -12.5

The x term is 29.5x.  Take half its coefficient (14.75).
Square it (217.5625) and add it to both sides.

Add '217.5625' to each side of the equation.
29.5x + 217.5625 + x2 = -12.5 + 217.5625

Reorder the terms:
217.5625 + 29.5x + x2 = -12.5 + 217.5625

Combine like terms: -12.5 + 217.5625 = 205.0625
217.5625 + 29.5x + x2 = 205.0625

Factor a perfect square on the left side:
(x + 14.75)(x + 14.75) = 205.0625

Calculate the square root of the right side: 14.320003492

Break this problem into two subproblems by setting 
(x + 14.75) equal to 14.320003492 and -14.320003492.


Subproblem 1
x + 14.75 = 14.320003492

Simplifying
x + 14.75 = 14.320003492

Reorder the terms:
14.75 + x = 14.320003492

Solving
14.75 + x = 14.320003492

Solving for variable 'x'.

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

Add '-14.75' to each side of the equation.
14.75 + -14.75 + x = 14.320003492 + -14.75

Combine like terms: 14.75 + -14.75 = 0.00
0.00 + x = 14.320003492 + -14.75
x = 14.320003492 + -14.75

Combine like terms: 14.320003492 + -14.75 = -0.429996508
x = -0.429996508

Simplifying
x = -0.429996508


Subproblem 2
x + 14.75 = -14.320003492

Simplifying
x + 14.75 = -14.320003492

Reorder the terms:
14.75 + x = -14.320003492

Solving
14.75 + x = -14.320003492

Solving for variable 'x'.

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

Add '-14.75' to each side of the equation.
14.75 + -14.75 + x = -14.320003492 + -14.75

Combine like terms: 14.75 + -14.75 = 0.00
0.00 + x = -14.320003492 + -14.75
x = -14.320003492 + -14.75

Combine like terms: -14.320003492 + -14.75 = -29.070003492
x = -29.070003492

Simplifying
x = -29.070003492


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.429996508, -29.070003492}
Solution
x = {-0.429996508, -29.070003492}

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