2x(x+1)+28=-4x

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Solution for 2x(x+1)+28=-4x equation: 


Simplifying
2x(x + 1) + 28 = -4x

Reorder the terms:
2x(1 + x) + 28 = -4x
(1 * 2x + x * 2x) + 28 = -4x
(2x + 2x2) + 28 = -4x

Reorder the terms:
28 + 2x + 2x2 = -4x

Solving
28 + 2x + 2x2 = -4x

Solving for variable 'x'.

Reorder the terms:
28 + 2x + 4x + 2x2 = -4x + 4x

Combine like terms: 2x + 4x = 6x
28 + 6x + 2x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
28 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(14 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
14 + 3x + x2 = 0

Solving
14 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 3x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + 3x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 3x + x2 = 0 + -14
3x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
3x + x2 = -14

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -14 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -14 + 2.25

Combine like terms: -14 + 2.25 = -11.75
2.25 + 3x + x2 = -11.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -11.75

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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