(w-4)(w-4)+11=36

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Solution for (w-4)(w-4)+11=36 equation: 


Simplifying
(w + -4)(w + -4) + 11 = 36

Reorder the terms:
(-4 + w)(w + -4) + 11 = 36

Reorder the terms:
(-4 + w)(-4 + w) + 11 = 36

Multiply (-4 + w) * (-4 + w)
(-4(-4 + w) + w(-4 + w)) + 11 = 36
((-4 * -4 + w * -4) + w(-4 + w)) + 11 = 36
((16 + -4w) + w(-4 + w)) + 11 = 36
(16 + -4w + (-4 * w + w * w)) + 11 = 36
(16 + -4w + (-4w + w2)) + 11 = 36

Combine like terms: -4w + -4w = -8w
(16 + -8w + w2) + 11 = 36

Reorder the terms:
16 + 11 + -8w + w2 = 36

Combine like terms: 16 + 11 = 27
27 + -8w + w2 = 36

Solving
27 + -8w + w2 = 36

Solving for variable 'w'.

Reorder the terms:
27 + -36 + -8w + w2 = 36 + -36

Combine like terms: 27 + -36 = -9
-9 + -8w + w2 = 36 + -36

Combine like terms: 36 + -36 = 0
-9 + -8w + w2 = 0

Factor a trinomial.
(-1 + -1w)(9 + -1w) = 0


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

Simplifying
-1 + -1w = 0

Solving
-1 + -1w = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1w = 0 + 1
-1w = 0 + 1

Combine like terms: 0 + 1 = 1
-1w = 1

Divide each side by '-1'.
w = -1

Simplifying
w = -1

Subproblem 2
Set the factor '(9 + -1w)' equal to zero and attempt to solve:

Simplifying
9 + -1w = 0

Solving
9 + -1w = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1w = 0 + -9
-1w = 0 + -9

Combine like terms: 0 + -9 = -9
-1w = -9

Divide each side by '-1'.
w = 9

Simplifying
w = 9
Solution
w = {-1, 9}

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