20x^2+2x-1=0

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


Simplifying
20x2 + 2x + -1 = 0

Reorder the terms:
-1 + 2x + 20x2 = 0

Solving
-1 + 2x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
-0.05 + 0.1x + x2 = 0

Move the constant term to the right:

Add '0.05' to each side of the equation.
-0.05 + 0.1x + 0.05 + x2 = 0 + 0.05

Reorder the terms:
-0.05 + 0.05 + 0.1x + x2 = 0 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + 0.1x + x2 = 0 + 0.05
0.1x + x2 = 0 + 0.05

Combine like terms: 0 + 0.05 = 0.05
0.1x + x2 = 0.05

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 = 0.05 + 0.0025

Reorder the terms:
0.0025 + 0.1x + x2 = 0.05 + 0.0025

Combine like terms: 0.05 + 0.0025 = 0.0525
0.0025 + 0.1x + x2 = 0.0525

Factor a perfect square on the left side:
(x + 0.05)(x + 0.05) = 0.0525

Calculate the square root of the right side: 0.229128785

Break this problem into two subproblems by setting 
(x + 0.05) equal to 0.229128785 and -0.229128785.

Subproblem 1

x + 0.05 = 0.229128785 Simplifying x + 0.05 = 0.229128785 Reorder the terms: 0.05 + x = 0.229128785 Solving 0.05 + x = 0.229128785 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 = 0.229128785 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.229128785 + -0.05 x = 0.229128785 + -0.05 Combine like terms: 0.229128785 + -0.05 = 0.179128785 x = 0.179128785 Simplifying x = 0.179128785

Subproblem 2

x + 0.05 = -0.229128785 Simplifying x + 0.05 = -0.229128785 Reorder the terms: 0.05 + x = -0.229128785 Solving 0.05 + x = -0.229128785 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 = -0.229128785 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.229128785 + -0.05 x = -0.229128785 + -0.05 Combine like terms: -0.229128785 + -0.05 = -0.279128785 x = -0.279128785 Simplifying x = -0.279128785

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.179128785, -0.279128785}

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