Solve by Factoring n^2-10n+22=-2

$n^{2} - 10 n + 22 = - 2$

Step 1

Add $2$ to both sides of the equation.

$n^{2} - 10 n + 22 + 2 = 0$

Step 2

Add $22$ and $2$ .

$n^{2} - 10 n + 24 = 0$

Step 3

Factor $n^{2} - 10 n + 24$ 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 $24$ and whose sum is $- 10$ .

$- 6, - 4$

Write the factored form using these integers.

$(n - 6) (n - 4) = 0$

Step 4

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

$n - 6 = 0$

$n - 4 = 0$

Step 5

Set $n - 6$ equal to $0$ and solve for $n$ .

Set $n - 6$ equal to $0$ .

$n - 6 = 0$

Add $6$ to both sides of the equation.

$n = 6$

Step 6

Set $n - 4$ equal to $0$ and solve for $n$ .

Set $n - 4$ equal to $0$ .

$n - 4 = 0$

Add $4$ to both sides of the equation.

$n = 4$

Step 7

The final solution is all the values that make $(n - 6) (n - 4) = 0$ true.

$n = 6, 4$

Solve by Factoring n^2-10n+22=-2

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