50x^2+20x+1=0

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Solution for 50x^2+20x+1=0 equation:


Simplifying
50x2 + 20x + 1 = 0

Reorder the terms:
1 + 20x + 50x2 = 0

Solving
1 + 20x + 50x2 = 0

Solving for variable 'x'.

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

Divide each side by '50'.
0.02 + 0.4x + x2 = 0

Move the constant term to the right:

Add '-0.02' to each side of the equation.
0.02 + 0.4x + -0.02 + x2 = 0 + -0.02

Reorder the terms:
0.02 + -0.02 + 0.4x + x2 = 0 + -0.02

Combine like terms: 0.02 + -0.02 = 0.00
0.00 + 0.4x + x2 = 0 + -0.02
0.4x + x2 = 0 + -0.02

Combine like terms: 0 + -0.02 = -0.02
0.4x + x2 = -0.02

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = -0.02 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = -0.02 + 0.04

Combine like terms: -0.02 + 0.04 = 0.02
0.04 + 0.4x + x2 = 0.02

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 0.02

Calculate the square root of the right side: 0.141421356

Break this problem into two subproblems by setting 
(x + 0.2) equal to 0.141421356 and -0.141421356.

Subproblem 1

x + 0.2 = 0.141421356 Simplifying x + 0.2 = 0.141421356 Reorder the terms: 0.2 + x = 0.141421356 Solving 0.2 + x = 0.141421356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.141421356 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.141421356 + -0.2 x = 0.141421356 + -0.2 Combine like terms: 0.141421356 + -0.2 = -0.058578644 x = -0.058578644 Simplifying x = -0.058578644

Subproblem 2

x + 0.2 = -0.141421356 Simplifying x + 0.2 = -0.141421356 Reorder the terms: 0.2 + x = -0.141421356 Solving 0.2 + x = -0.141421356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.141421356 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.141421356 + -0.2 x = -0.141421356 + -0.2 Combine like terms: -0.141421356 + -0.2 = -0.341421356 x = -0.341421356 Simplifying x = -0.341421356

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.058578644, -0.341421356}

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