Solve by Factoring x^2=5x+24

$x^{2} = 5 x + 24$

Step 1

Move all the expressions to the left side of the equation.

Subtract $5 x$ from both sides of the equation.

$x^{2} - 5 x = 24$

Subtract $24$ from both sides of the equation.

$x^{2} - 5 x - 24 = 0$

Step 2

Factor $x^{2} - 5 x - 24$ 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 $- 5$ .

$- 8, 3$

Write the factored form using these integers.

$(x - 8) (x + 3) = 0$

Step 3

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

$x - 8 = 0$

$x + 3 = 0$

Step 4

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Step 5

Set $x + 3$ equal to $0$ and solve for $x$ .

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 6

The final solution is all the values that make $(x - 8) (x + 3) = 0$ true.

$x = 8, - 3$

Solve by Factoring x^2=5x+24

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