Solve by Factoring s^2-14s+45=0

$s^{2} - 14 s + 45 = 0$

Step 1

Factor $s^{2} - 14 s + 45$ 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 $45$ and whose sum is $- 14$ .

$- 9, - 5$

Write the factored form using these integers.

$(s - 9) (s - 5) = 0$

Step 2

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

$s - 9 = 0$

$s - 5 = 0$

Step 3

Set $s - 9$ equal to $0$ and solve for $s$ .

Set $s - 9$ equal to $0$ .

$s - 9 = 0$

Add $9$ to both sides of the equation.

$s = 9$

Step 4

Set $s - 5$ equal to $0$ and solve for $s$ .

Set $s - 5$ equal to $0$ .

$s - 5 = 0$

Add $5$ to both sides of the equation.

$s = 5$

Step 5

The final solution is all the values that make $(s - 9) (s - 5) = 0$ true.

$s = 9, 5$

Solve by Factoring s^2-14s+45=0

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