Algebra Examples

$g (r) = r^{2} - 6 r - 55$

Step 1

Set $r^{2} - 6 r - 55$ equal to $0$ .

$r^{2} - 6 r - 55 = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Factor $r^{2} - 6 r - 55$ using the AC method.

Tap for more steps...

Step 2.1.1

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 $- 55$ and whose sum is $- 6$ .

$- 11, 5$

Step 2.1.2

Write the factored form using these integers.

$(r - 11) (r + 5) = 0$

Step 2.2

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

$r - 11 = 0$

$r + 5 = 0$

Step 2.3

Set $r - 11$ equal to $0$ and solve for $r$ .

Tap for more steps...

Step 2.3.1

Set $r - 11$ equal to $0$ .

$r - 11 = 0$

Step 2.3.2

Add $11$ to both sides of the equation.

$r = 11$

Step 2.4

Set $r + 5$ equal to $0$ and solve for $r$ .

Tap for more steps...

Step 2.4.1

Set $r + 5$ equal to $0$ .

$r + 5 = 0$

Step 2.4.2

Subtract $5$ from both sides of the equation.

$r = - 5$

Step 2.5

The final solution is all the values that make $(r - 11) (r + 5) = 0$ true.

$r = 11, - 5$

Step 3