100x^2+10x-4=0

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Solution for 100x^2+10x-4=0 equation: 


Simplifying
100x2 + 10x + -4 = 0

Reorder the terms:
-4 + 10x + 100x2 = 0

Solving
-4 + 10x + 100x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 5x + 50x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 5x + 50x2)' equal to zero and attempt to solve:

Simplifying
-2 + 5x + 50x2 = 0

Solving
-2 + 5x + 50x2 = 0

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

Divide each side by '50'.
-0.04 + 0.1x + x2 = 0.0

Move the constant term to the right:

Add '0.04' to each side of the equation.
-0.04 + 0.1x + 0.04 + x2 = 0.0 + 0.04

Reorder the terms:
-0.04 + 0.04 + 0.1x + x2 = 0.0 + 0.04

Combine like terms: -0.04 + 0.04 = 0.00
0.00 + 0.1x + x2 = 0.0 + 0.04
0.1x + x2 = 0.0 + 0.04

Combine like terms: 0.0 + 0.04 = 0.04
0.1x + x2 = 0.04

The x term is 0.1x.  Take half its coefficient (0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
0.1x + 0.0025 + x2 = 0.04 + 0.0025

Reorder the terms:
0.0025 + 0.1x + x2 = 0.04 + 0.0025

Combine like terms: 0.04 + 0.0025 = 0.0425
0.0025 + 0.1x + x2 = 0.0425

Factor a perfect square on the left side:
(x + 0.05)(x + 0.05) = 0.0425

Calculate the square root of the right side: 0.206155281

Break this problem into two subproblems by setting 
(x + 0.05) equal to 0.206155281 and -0.206155281.


Subproblem 1
x + 0.05 = 0.206155281

Simplifying
x + 0.05 = 0.206155281

Reorder the terms:
0.05 + x = 0.206155281

Solving
0.05 + x = 0.206155281

Solving for variable 'x'.

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

Add '-0.05' to each side of the equation.
0.05 + -0.05 + x = 0.206155281 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + x = 0.206155281 + -0.05
x = 0.206155281 + -0.05

Combine like terms: 0.206155281 + -0.05 = 0.156155281
x = 0.156155281

Simplifying
x = 0.156155281


Subproblem 2
x + 0.05 = -0.206155281

Simplifying
x + 0.05 = -0.206155281

Reorder the terms:
0.05 + x = -0.206155281

Solving
0.05 + x = -0.206155281

Solving for variable 'x'.

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

Add '-0.05' to each side of the equation.
0.05 + -0.05 + x = -0.206155281 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + x = -0.206155281 + -0.05
x = -0.206155281 + -0.05

Combine like terms: -0.206155281 + -0.05 = -0.256155281
x = -0.256155281

Simplifying
x = -0.256155281


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.156155281, -0.256155281}
Solution
x = {0.156155281, -0.256155281}

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