5x^2+10x+1=0

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Solution for 5x^2+10x+1=0 equation:


Simplifying
5x2 + 10x + 1 = 0

Reorder the terms:
1 + 10x + 5x2 = 0

Solving
1 + 10x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
0.2 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 2x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 2x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 2x + x2 = 0 + -0.2
2x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
2x + x2 = -0.2

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.2 + 1

Reorder the terms:
1 + 2x + x2 = -0.2 + 1

Combine like terms: -0.2 + 1 = 0.8
1 + 2x + x2 = 0.8

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.8

Calculate the square root of the right side: 0.894427191

Break this problem into two subproblems by setting 
(x + 1) equal to 0.894427191 and -0.894427191.

Subproblem 1

x + 1 = 0.894427191 Simplifying x + 1 = 0.894427191 Reorder the terms: 1 + x = 0.894427191 Solving 1 + x = 0.894427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.894427191 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.894427191 + -1 x = 0.894427191 + -1 Combine like terms: 0.894427191 + -1 = -0.105572809 x = -0.105572809 Simplifying x = -0.105572809

Subproblem 2

x + 1 = -0.894427191 Simplifying x + 1 = -0.894427191 Reorder the terms: 1 + x = -0.894427191 Solving 1 + x = -0.894427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.894427191 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.894427191 + -1 x = -0.894427191 + -1 Combine like terms: -0.894427191 + -1 = -1.894427191 x = -1.894427191 Simplifying x = -1.894427191

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.105572809, -1.894427191}

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