2w^2+19w+53=(w+7)

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Solution for 2w^2+19w+53=(w+7) equation: 


Simplifying
2w2 + 19w + 53 = (w + 7)

Reorder the terms:
53 + 19w + 2w2 = (w + 7)

Reorder the terms:
53 + 19w + 2w2 = (7 + w)

Remove parenthesis around (7 + w)
53 + 19w + 2w2 = 7 + w

Solving
53 + 19w + 2w2 = 7 + w

Solving for variable 'w'.

Reorder the terms:
53 + -7 + 19w + -1w + 2w2 = 7 + w + -7 + -1w

Combine like terms: 53 + -7 = 46
46 + 19w + -1w + 2w2 = 7 + w + -7 + -1w

Combine like terms: 19w + -1w = 18w
46 + 18w + 2w2 = 7 + w + -7 + -1w

Reorder the terms:
46 + 18w + 2w2 = 7 + -7 + w + -1w

Combine like terms: 7 + -7 = 0
46 + 18w + 2w2 = 0 + w + -1w
46 + 18w + 2w2 = w + -1w

Combine like terms: w + -1w = 0
46 + 18w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(23 + 9w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(23 + 9w + w2)' equal to zero and attempt to solve:

Simplifying
23 + 9w + w2 = 0

Solving
23 + 9w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + 9w + -23 + w2 = 0 + -23

Reorder the terms:
23 + -23 + 9w + w2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 9w + w2 = 0 + -23
9w + w2 = 0 + -23

Combine like terms: 0 + -23 = -23
9w + w2 = -23

The w term is 9w.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9w + 20.25 + w2 = -23 + 20.25

Reorder the terms:
20.25 + 9w + w2 = -23 + 20.25

Combine like terms: -23 + 20.25 = -2.75
20.25 + 9w + w2 = -2.75

Factor a perfect square on the left side:
(w + 4.5)(w + 4.5) = -2.75

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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