2x-x(x+5)=6+(x+1)

Solution for 2x-x(x+5)=6+(x+1) equation:

Simplifying
2x + -1x(x + 5) = 6 + (x + 1)

Reorder the terms:
2x + -1x(5 + x) = 6 + (x + 1)
2x + (5 * -1x + x * -1x) = 6 + (x + 1)
2x + (-5x + -1x2) = 6 + (x + 1)

Combine like terms: 2x + -5x = -3x
-3x + -1x2 = 6 + (x + 1)

Reorder the terms:
-3x + -1x2 = 6 + (1 + x)

Remove parenthesis around (1 + x)
-3x + -1x2 = 6 + 1 + x

Combine like terms: 6 + 1 = 7
-3x + -1x2 = 7 + x

Solving
-3x + -1x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
-7 + -3x + -1x + -1x2 = 7 + x + -7 + -1x

Combine like terms: -3x + -1x = -4x
-7 + -4x + -1x2 = 7 + x + -7 + -1x

Reorder the terms:
-7 + -4x + -1x2 = 7 + -7 + x + -1x

Combine like terms: 7 + -7 = 0
-7 + -4x + -1x2 = 0 + x + -1x
-7 + -4x + -1x2 = x + -1x

Combine like terms: x + -1x = 0
-7 + -4x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 4x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
7 + 4x + x2 = 0

Solving
7 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 4x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 4x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4x + x2 = 0 + -7
4x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
4x + x2 = -7

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -7 + 4

Reorder the terms:
4 + 4x + x2 = -7 + 4

Combine like terms: -7 + 4 = -3
4 + 4x + x2 = -3

Factor a perfect square on the left side:
(x + 2)(x + 2) = -3

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.