(5x+1)(x+1)+1=0

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Solution for (5x+1)(x+1)+1=0 equation: 


Simplifying
(5x + 1)(x + 1) + 1 = 0

Reorder the terms:
(1 + 5x)(x + 1) + 1 = 0

Reorder the terms:
(1 + 5x)(1 + x) + 1 = 0

Multiply (1 + 5x) * (1 + x)
(1(1 + x) + 5x * (1 + x)) + 1 = 0
((1 * 1 + x * 1) + 5x * (1 + x)) + 1 = 0
((1 + 1x) + 5x * (1 + x)) + 1 = 0
(1 + 1x + (1 * 5x + x * 5x)) + 1 = 0
(1 + 1x + (5x + 5x2)) + 1 = 0

Combine like terms: 1x + 5x = 6x
(1 + 6x + 5x2) + 1 = 0

Reorder the terms:
1 + 1 + 6x + 5x2 = 0

Combine like terms: 1 + 1 = 2
2 + 6x + 5x2 = 0

Solving
2 + 6x + 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'.
0.4 + 1.2x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 1.2x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 1.2x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 1.2x + x2 = 0 + -0.4
1.2x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
1.2x + x2 = -0.4

The x term is 1.2x.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2x + 0.36 + x2 = -0.4 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = -0.4 + 0.36

Combine like terms: -0.4 + 0.36 = -0.04
0.36 + 1.2x + x2 = -0.04

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = -0.04

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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