(w-5)*(w-5)=9

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Solution for (w-5)*(w-5)=9 equation:


Simplifying
(w + -5)(w + -5) = 9

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

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

Multiply (-5 + w) * (-5 + w)
(-5(-5 + w) + w(-5 + w)) = 9
((-5 * -5 + w * -5) + w(-5 + w)) = 9
((25 + -5w) + w(-5 + w)) = 9
(25 + -5w + (-5 * w + w * w)) = 9
(25 + -5w + (-5w + w2)) = 9

Combine like terms: -5w + -5w = -10w
(25 + -10w + w2) = 9

Solving
25 + -10w + w2 = 9

Solving for variable 'w'.

Reorder the terms:
25 + -9 + -10w + w2 = 9 + -9

Combine like terms: 25 + -9 = 16
16 + -10w + w2 = 9 + -9

Combine like terms: 9 + -9 = 0
16 + -10w + w2 = 0

Factor a trinomial.
(2 + -1w)(8 + -1w) = 0


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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 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 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2

Subproblem 2
Set the factor '(8 + -1w)' equal to zero and attempt to solve:

Simplifying
8 + -1w = 0

Solving
8 + -1w = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1w = 0 + -8

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

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

Divide each side by '-1'.
w = 8

Simplifying
w = 8
Solution
w = {2, 8}

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