Solve for a a^2-28a+192=0

$a^{2} - 28 a + 192 = 0$

Step 1

Factor $a^{2} - 28 a + 192$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $192$ and whose sum is $- 28$ .

$- 16, - 12$

Write the factored form using these integers.

$(a - 16) (a - 12) = 0$

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$a - 16 = 0$

$a - 12 = 0$

Step 3

Set $a - 16$ equal to $0$ and solve for $a$ .

Set $a - 16$ equal to $0$ .

$a - 16 = 0$

Add $16$ to both sides of the equation.

$a = 16$

Step 4

Set $a - 12$ equal to $0$ and solve for $a$ .

Set $a - 12$ equal to $0$ .

$a - 12 = 0$

Add $12$ to both sides of the equation.

$a = 12$

Step 5

The final solution is all the values that make $(a - 16) (a - 12) = 0$ true.

$a = 16, 12$

Solve for a a^2-28a+192=0

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