(w+5)(w+5)=2(w^2)+16w+33

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Solution for (w+5)(w+5)=2(w^2)+16w+33 equation:


Simplifying
(w + 5)(w + 5) = 2(w2) + 16w + 33

Reorder the terms:
(5 + w)(w + 5) = 2(w2) + 16w + 33

Reorder the terms:
(5 + w)(5 + w) = 2(w2) + 16w + 33

Multiply (5 + w) * (5 + w)
(5(5 + w) + w(5 + w)) = 2(w2) + 16w + 33
((5 * 5 + w * 5) + w(5 + w)) = 2(w2) + 16w + 33
((25 + 5w) + w(5 + w)) = 2(w2) + 16w + 33
(25 + 5w + (5 * w + w * w)) = 2(w2) + 16w + 33
(25 + 5w + (5w + w2)) = 2(w2) + 16w + 33

Combine like terms: 5w + 5w = 10w
(25 + 10w + w2) = 2(w2) + 16w + 33

Reorder the terms:
25 + 10w + w2 = 33 + 16w + 2w2

Solving
25 + 10w + w2 = 33 + 16w + 2w2

Solving for variable 'w'.

Reorder the terms:
25 + -33 + 10w + -16w + w2 + -2w2 = 33 + 16w + 2w2 + -33 + -16w + -2w2

Combine like terms: 25 + -33 = -8
-8 + 10w + -16w + w2 + -2w2 = 33 + 16w + 2w2 + -33 + -16w + -2w2

Combine like terms: 10w + -16w = -6w
-8 + -6w + w2 + -2w2 = 33 + 16w + 2w2 + -33 + -16w + -2w2

Combine like terms: w2 + -2w2 = -1w2
-8 + -6w + -1w2 = 33 + 16w + 2w2 + -33 + -16w + -2w2

Reorder the terms:
-8 + -6w + -1w2 = 33 + -33 + 16w + -16w + 2w2 + -2w2

Combine like terms: 33 + -33 = 0
-8 + -6w + -1w2 = 0 + 16w + -16w + 2w2 + -2w2
-8 + -6w + -1w2 = 16w + -16w + 2w2 + -2w2

Combine like terms: 16w + -16w = 0
-8 + -6w + -1w2 = 0 + 2w2 + -2w2
-8 + -6w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-8 + -6w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 6w + w2) = 0

Factor a trinomial.
-1((4 + w)(2 + w)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

Solving
4 + w = 0

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

Add '-4' to each side of the equation.
4 + -4 + w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + w = 0 + -4
w = 0 + -4

Combine like terms: 0 + -4 = -4
w = -4

Simplifying
w = -4

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 = {-4, -2}

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