196x^2+98x+2=0

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Solution for 196x^2+98x+2=0 equation: 


Simplifying
196x2 + 98x + 2 = 0

Reorder the terms:
2 + 98x + 196x2 = 0

Solving
2 + 98x + 196x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 49x + 98x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 49x + 98x2)' equal to zero and attempt to solve:

Simplifying
1 + 49x + 98x2 = 0

Solving
1 + 49x + 98x2 = 0

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

Divide each side by '98'.
0.01020408163 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-0.01020408163' to each side of the equation.
0.01020408163 + 0.5x + -0.01020408163 + x2 = 0 + -0.01020408163

Reorder the terms:
0.01020408163 + -0.01020408163 + 0.5x + x2 = 0 + -0.01020408163

Combine like terms: 0.01020408163 + -0.01020408163 = 0.00000000000
0.00000000000 + 0.5x + x2 = 0 + -0.01020408163
0.5x + x2 = 0 + -0.01020408163

Combine like terms: 0 + -0.01020408163 = -0.01020408163
0.5x + x2 = -0.01020408163

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 = -0.01020408163 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -0.01020408163 + 0.0625

Combine like terms: -0.01020408163 + 0.0625 = 0.05229591837
0.0625 + 0.5x + x2 = 0.05229591837

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.05229591837

Calculate the square root of the right side: 0.228683008

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.228683008 and -0.228683008.


Subproblem 1
x + 0.25 = 0.228683008

Simplifying
x + 0.25 = 0.228683008

Reorder the terms:
0.25 + x = 0.228683008

Solving
0.25 + x = 0.228683008

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 = 0.228683008 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.228683008 + -0.25
x = 0.228683008 + -0.25

Combine like terms: 0.228683008 + -0.25 = -0.021316992
x = -0.021316992

Simplifying
x = -0.021316992


Subproblem 2
x + 0.25 = -0.228683008

Simplifying
x + 0.25 = -0.228683008

Reorder the terms:
0.25 + x = -0.228683008

Solving
0.25 + x = -0.228683008

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 = -0.228683008 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.228683008 + -0.25
x = -0.228683008 + -0.25

Combine like terms: -0.228683008 + -0.25 = -0.478683008
x = -0.478683008

Simplifying
x = -0.478683008


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.021316992, -0.478683008}
Solution
x = {-0.021316992, -0.478683008}

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