Solve by factoring
x^2 -2x -24=0
(x-6)(x+4)=0
You finish.
To solve the quadratic equation by factoring, you need to find two binomials whose product is equal to zero. Let's factor the given equation:
x^2 - 2x - 24 = 0
First, observe the constant term (-24, in this case). We need to determine which two numbers multiply to give -24 and add up to -2 (the coefficient of the x term).
The factors of -24 are:
-1, 24
-2, 12
-3, 8
-4, 6
Among these pairs, the pair that adds up to -2 is -4 and 6. Therefore, we can rewrite the equation as:
(x - 6)(x + 4) = 0
Now, we have factored the quadratic equation. To solve for x, we can set each factor equal to zero and solve for x separately:
Setting x - 6 = 0:
x = 6
Setting x + 4 = 0:
x = -4
Thus, the solutions to the equation x^2 - 2x - 24 = 0 are x = 6 and x = -4.