6=x^2+2x+11

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Solution for 6=x^2+2x+11 equation: 


Simplifying
6 = x2 + 2x + 11

Reorder the terms:
6 = 11 + 2x + x2

Solving
6 = 11 + 2x + x2

Solving for variable 'x'.

Combine like terms: 6 + -11 = -5
-5 + -2x + -1x2 = 11 + 2x + x2 + -11 + -2x + -1x2

Reorder the terms:
-5 + -2x + -1x2 = 11 + -11 + 2x + -2x + x2 + -1x2

Combine like terms: 11 + -11 = 0
-5 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2
-5 + -2x + -1x2 = 2x + -2x + x2 + -1x2

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 2x + x2) = 0

Ignore the factor -1.

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

Simplifying
5 + 2x + x2 = 0

Solving
5 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 2x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 2x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x + x2 = 0 + -5
2x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
2x + x2 = -5

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 = -5 + 1

Reorder the terms:
1 + 2x + x2 = -5 + 1

Combine like terms: -5 + 1 = -4
1 + 2x + x2 = -4

Factor a perfect square on the left side:
(x + 1)(x + 1) = -4

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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