2x^2+5x=x-6

Solution for 2x^2+5x=x-6 equation:

Simplifying
2x2 + 5x = x + -6

Reorder the terms:
5x + 2x2 = x + -6

Reorder the terms:
5x + 2x2 = -6 + x

Solving
5x + 2x2 = -6 + x

Solving for variable 'x'.

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

Combine like terms: 5x + -1x = 4x
6 + 4x + 2x2 = -6 + x + 6 + -1x

Reorder the terms:
6 + 4x + 2x2 = -6 + 6 + x + -1x

Combine like terms: -6 + 6 = 0
6 + 4x + 2x2 = 0 + x + -1x
6 + 4x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
6 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
3 + 2x + x2 = 0

Solving
3 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 2x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 2x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x + x2 = 0 + -3
2x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
2x + x2 = -3

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 = -3 + 1

Reorder the terms:
1 + 2x + x2 = -3 + 1

Combine like terms: -3 + 1 = -2
1 + 2x + x2 = -2

Factor a perfect square on the left side:
(x + 1)(x + 1) = -2

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.