2w^2+w=-28

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Solution for 2w^2+w=-28 equation:


Simplifying
2w2 + w = -28

Reorder the terms:
w + 2w2 = -28

Solving
w + 2w2 = -28

Solving for variable 'w'.

Reorder the terms:
28 + w + 2w2 = -28 + 28

Combine like terms: -28 + 28 = 0
28 + w + 2w2 = 0

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

Divide each side by '2'.
14 + 0.5w + w2 = 0

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 0.5w + -14 + w2 = 0 + -14

Reorder the terms:
14 + -14 + 0.5w + w2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 0.5w + w2 = 0 + -14
0.5w + w2 = 0 + -14

Combine like terms: 0 + -14 = -14
0.5w + w2 = -14

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5w + 0.25 + w2 = -14 + 0.25

Reorder the terms:
0.25 + 0.5w + w2 = -14 + 0.25

Combine like terms: -14 + 0.25 = -13.75
0.25 + 0.5w + w2 = -13.75

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = -13.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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