(w-10)*(w-10)=49

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Solution for (w-10)*(w-10)=49 equation: 


Simplifying
(w + -10)(w + -10) = 49

Reorder the terms:
(-10 + w)(w + -10) = 49

Reorder the terms:
(-10 + w)(-10 + w) = 49

Multiply (-10 + w) * (-10 + w)
(-10(-10 + w) + w(-10 + w)) = 49
((-10 * -10 + w * -10) + w(-10 + w)) = 49
((100 + -10w) + w(-10 + w)) = 49
(100 + -10w + (-10 * w + w * w)) = 49
(100 + -10w + (-10w + w2)) = 49

Combine like terms: -10w + -10w = -20w
(100 + -20w + w2) = 49

Solving
100 + -20w + w2 = 49

Solving for variable 'w'.

Reorder the terms:
100 + -49 + -20w + w2 = 49 + -49

Combine like terms: 100 + -49 = 51
51 + -20w + w2 = 49 + -49

Combine like terms: 49 + -49 = 0
51 + -20w + w2 = 0

Factor a trinomial.
(3 + -1w)(17 + -1w) = 0


Subproblem 1
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3

Subproblem 2
Set the factor '(17 + -1w)' equal to zero and attempt to solve:

Simplifying
17 + -1w = 0

Solving
17 + -1w = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1w = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1w = 0 + -17
-1w = 0 + -17

Combine like terms: 0 + -17 = -17
-1w = -17

Divide each side by '-1'.
w = 17

Simplifying
w = 17
Solution
w = {3, 17}

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