2w^2+22w+61=(w+7)(w+7)

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Solution for 2w^2+22w+61=(w+7)(w+7) equation: 


Simplifying
2w2 + 22w + 61 = (w + 7)(w + 7)

Reorder the terms:
61 + 22w + 2w2 = (w + 7)(w + 7)

Reorder the terms:
61 + 22w + 2w2 = (7 + w)(w + 7)

Reorder the terms:
61 + 22w + 2w2 = (7 + w)(7 + w)

Multiply (7 + w) * (7 + w)
61 + 22w + 2w2 = (7(7 + w) + w(7 + w))
61 + 22w + 2w2 = ((7 * 7 + w * 7) + w(7 + w))
61 + 22w + 2w2 = ((49 + 7w) + w(7 + w))
61 + 22w + 2w2 = (49 + 7w + (7 * w + w * w))
61 + 22w + 2w2 = (49 + 7w + (7w + w2))

Combine like terms: 7w + 7w = 14w
61 + 22w + 2w2 = (49 + 14w + w2)

Solving
61 + 22w + 2w2 = 49 + 14w + w2

Solving for variable 'w'.

Reorder the terms:
61 + -49 + 22w + -14w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Combine like terms: 61 + -49 = 12
12 + 22w + -14w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Combine like terms: 22w + -14w = 8w
12 + 8w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
12 + 8w + 1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Reorder the terms:
12 + 8w + 1w2 = 49 + -49 + 14w + -14w + w2 + -1w2

Combine like terms: 49 + -49 = 0
12 + 8w + 1w2 = 0 + 14w + -14w + w2 + -1w2
12 + 8w + 1w2 = 14w + -14w + w2 + -1w2

Combine like terms: 14w + -14w = 0
12 + 8w + 1w2 = 0 + w2 + -1w2
12 + 8w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
12 + 8w + 1w2 = 0

Factor a trinomial.
(6 + w)(2 + w) = 0


Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6

Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + w = 0 + -2

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

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

Simplifying
w = -2
Solution
w = {-6, -2}

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