(a-5)(a-5)=196

Solution for (a-5)(a-5)=196 equation:

Simplifying
(a + -5)(a + -5) = 196

Reorder the terms:
(-5 + a)(a + -5) = 196

Reorder the terms:
(-5 + a)(-5 + a) = 196

Multiply (-5 + a) * (-5 + a)
(-5(-5 + a) + a(-5 + a)) = 196
((-5 * -5 + a * -5) + a(-5 + a)) = 196
((25 + -5a) + a(-5 + a)) = 196
(25 + -5a + (-5 * a + a * a)) = 196
(25 + -5a + (-5a + a2)) = 196

Combine like terms: -5a + -5a = -10a
(25 + -10a + a2) = 196

Solving
25 + -10a + a2 = 196

Solving for variable 'a'.

Reorder the terms:
25 + -196 + -10a + a2 = 196 + -196

Combine like terms: 25 + -196 = -171
-171 + -10a + a2 = 196 + -196

Combine like terms: 196 + -196 = 0
-171 + -10a + a2 = 0

Factor a trinomial.
(-9 + -1a)(19 + -1a) = 0

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

Simplifying
-9 + -1a = 0

Solving
-9 + -1a = 0

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

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

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

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

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

Simplifying
a = -9
Subproblem 2
Set the factor '(19 + -1a)' equal to zero and attempt to solve:

Simplifying
19 + -1a = 0

Solving
19 + -1a = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1a = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1a = 0 + -19
-1a = 0 + -19

Combine like terms: 0 + -19 = -19
-1a = -19

Divide each side by '-1'.
a = 19

Simplifying
a = 19
Solution
a = {-9, 19}