.2[(x+1)(x+1)]+10=0

Solution for .2[(x+1)(x+1)]+10=0 equation:

Simplifying
0.2[(x + 1)(x + 1)] + 10 = 0

Reorder the terms:
0.2[(1 + x)(x + 1)] + 10 = 0

Reorder the terms:
0.2[(1 + x)(1 + x)] + 10 = 0

Multiply (1 + x) * (1 + x)
0.2[(1(1 + x) + x(1 + x))] + 10 = 0
0.2[((1 * 1 + x * 1) + x(1 + x))] + 10 = 0
0.2[((1 + 1x) + x(1 + x))] + 10 = 0
0.2[(1 + 1x + (1 * x + x * x))] + 10 = 0
0.2[(1 + 1x + (1x + x2))] + 10 = 0

Combine like terms: 1x + 1x = 2x
0.2[(1 + 2x + x2)] + 10 = 0
[1 * 0.2 + 2x * 0.2 + x2 * 0.2] + 10 = 0
[0.2 + 0.4x + 0.2x2] + 10 = 0

Reorder the terms:
0.2 + 10 + 0.4x + 0.2x2 = 0

Combine like terms: 0.2 + 10 = 10.2
10.2 + 0.4x + 0.2x2 = 0

Solving
10.2 + 0.4x + 0.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.2'.
51 + 2x + x2 = 0

Move the constant term to the right:

Add '-51' to each side of the equation.
51 + 2x + -51 + x2 = 0 + -51

Reorder the terms:
51 + -51 + 2x + x2 = 0 + -51

Combine like terms: 51 + -51 = 0
0 + 2x + x2 = 0 + -51
2x + x2 = 0 + -51

Combine like terms: 0 + -51 = -51
2x + x2 = -51

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 = -51 + 1

Reorder the terms:
1 + 2x + x2 = -51 + 1

Combine like terms: -51 + 1 = -50
1 + 2x + x2 = -50

Factor a perfect square on the left side:
(x + 1)(x + 1) = -50

Can't calculate square root of the right side.

The solution to this equation could not be determined.