10x^2+x^2+4x+4=x^2

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Solution for 10x^2+x^2+4x+4=x^2 equation:


Simplifying
10x2 + x2 + 4x + 4 = x2

Reorder the terms:
4 + 4x + 10x2 + x2 = x2

Combine like terms: 10x2 + x2 = 11x2
4 + 4x + 11x2 = x2

Solving
4 + 4x + 11x2 = x2

Solving for variable 'x'.

Combine like terms: 11x2 + -1x2 = 10x2
4 + 4x + 10x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + 4x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 2x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + 2x + 5x2)' equal to zero and attempt to solve:

Simplifying
2 + 2x + 5x2 = 0

Solving
2 + 2x + 5x2 = 0

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

Divide each side by '5'.
0.4 + 0.4x + x2 = 0

Move the constant term to the right:

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

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

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

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

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 = -0.4 + 0.04

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

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

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = -0.36

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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