100x^2+50x+3=0

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Solution for 100x^2+50x+3=0 equation: 


Simplifying
100x2 + 50x + 3 = 0

Reorder the terms:
3 + 50x + 100x2 = 0

Solving
3 + 50x + 100x2 = 0

Solving for variable 'x'.

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

Divide each side by '100'.
0.03 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-0.03' to each side of the equation.
0.03 + 0.5x + -0.03 + x2 = 0 + -0.03

Reorder the terms:
0.03 + -0.03 + 0.5x + x2 = 0 + -0.03

Combine like terms: 0.03 + -0.03 = 0.00
0.00 + 0.5x + x2 = 0 + -0.03
0.5x + x2 = 0 + -0.03

Combine like terms: 0 + -0.03 = -0.03
0.5x + x2 = -0.03

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = -0.03 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -0.03 + 0.0625

Combine like terms: -0.03 + 0.0625 = 0.0325
0.0625 + 0.5x + x2 = 0.0325

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.0325

Calculate the square root of the right side: 0.180277564

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.180277564 and -0.180277564.


Subproblem 1
x + 0.25 = 0.180277564

Simplifying
x + 0.25 = 0.180277564

Reorder the terms:
0.25 + x = 0.180277564

Solving
0.25 + x = 0.180277564

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.180277564 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.180277564 + -0.25
x = 0.180277564 + -0.25

Combine like terms: 0.180277564 + -0.25 = -0.069722436
x = -0.069722436

Simplifying
x = -0.069722436


Subproblem 2
x + 0.25 = -0.180277564

Simplifying
x + 0.25 = -0.180277564

Reorder the terms:
0.25 + x = -0.180277564

Solving
0.25 + x = -0.180277564

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.180277564 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.180277564 + -0.25
x = -0.180277564 + -0.25

Combine like terms: -0.180277564 + -0.25 = -0.430277564
x = -0.430277564

Simplifying
x = -0.430277564


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.069722436, -0.430277564}

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