Algebra Examples

$j^{2} + 10 j - 28 = 11$

Subtract $11$ from both sides of the equation.

$j^{2} + 10 j - 28 - 11 = 0$

Subtract $11$ from $- 28$ .

$j^{2} + 10 j - 39 = 0$

Factor $j^{2} + 10 j - 39$ using the AC method.

Tap for more steps...

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 $- 39$ and whose sum is $10$ .

$- 3, 13$

Write the factored form using these integers.

$(j - 3) (j + 13) = 0$

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

$j - 3 = 0$

$j + 13 = 0$

Set $j - 3$ equal to $0$ and solve for $j$ .

Tap for more steps...

Set $j - 3$ equal to $0$ .

$j - 3 = 0$

Add $3$ to both sides of the equation.

$j = 3$

Set $j + 13$ equal to $0$ and solve for $j$ .

Tap for more steps...

Set $j + 13$ equal to $0$ .

$j + 13 = 0$

Subtract $13$ from both sides of the equation.

$j = - 13$

The final solution is all the values that make $(j - 3) (j + 13) = 0$ true.

$j = 3, - 13$