2w^2-9w+19=(w-5)+(w-5)

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Solution for 2w^2-9w+19=(w-5)+(w-5) equation: 


Simplifying
2w2 + -9w + 19 = (w + -5) + (w + -5)

Reorder the terms:
19 + -9w + 2w2 = (w + -5) + (w + -5)

Reorder the terms:
19 + -9w + 2w2 = (-5 + w) + (w + -5)

Remove parenthesis around (-5 + w)
19 + -9w + 2w2 = -5 + w + (w + -5)

Reorder the terms:
19 + -9w + 2w2 = -5 + w + (-5 + w)

Remove parenthesis around (-5 + w)
19 + -9w + 2w2 = -5 + w + -5 + w

Reorder the terms:
19 + -9w + 2w2 = -5 + -5 + w + w

Combine like terms: -5 + -5 = -10
19 + -9w + 2w2 = -10 + w + w

Combine like terms: w + w = 2w
19 + -9w + 2w2 = -10 + 2w

Solving
19 + -9w + 2w2 = -10 + 2w

Solving for variable 'w'.

Reorder the terms:
19 + 10 + -9w + -2w + 2w2 = -10 + 2w + 10 + -2w

Combine like terms: 19 + 10 = 29
29 + -9w + -2w + 2w2 = -10 + 2w + 10 + -2w

Combine like terms: -9w + -2w = -11w
29 + -11w + 2w2 = -10 + 2w + 10 + -2w

Reorder the terms:
29 + -11w + 2w2 = -10 + 10 + 2w + -2w

Combine like terms: -10 + 10 = 0
29 + -11w + 2w2 = 0 + 2w + -2w
29 + -11w + 2w2 = 2w + -2w

Combine like terms: 2w + -2w = 0
29 + -11w + 2w2 = 0

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

Divide each side by '2'.
14.5 + -5.5w + w2 = 0

Move the constant term to the right:

Add '-14.5' to each side of the equation.
14.5 + -5.5w + -14.5 + w2 = 0 + -14.5

Reorder the terms:
14.5 + -14.5 + -5.5w + w2 = 0 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + -5.5w + w2 = 0 + -14.5
-5.5w + w2 = 0 + -14.5

Combine like terms: 0 + -14.5 = -14.5
-5.5w + w2 = -14.5

The w term is -5.5w.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5w + 7.5625 + w2 = -14.5 + 7.5625

Reorder the terms:
7.5625 + -5.5w + w2 = -14.5 + 7.5625

Combine like terms: -14.5 + 7.5625 = -6.9375
7.5625 + -5.5w + w2 = -6.9375

Factor a perfect square on the left side:
(w + -2.75)(w + -2.75) = -6.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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