For what values of x is x2 + 2x = 24 true?

To find the values of ( x ) for which ( x^2 + 2x = 24 ) is true, we can start by rearranging the equation:

1. Set the equation to 0:

[

x^2 + 2x – 24 = 0

]

2. Now, we can factor the quadratic equation. We need two numbers that multiply to -24 and add to 2. These numbers are 6 and -4.
[

(x + 6)(x – 4) = 0

]

3. Set each factor to zero:

[

x + 6 = 0 quad text{or} quad x – 4 = 0

]

4. Solve for ( x ):

[

x = -6 quad text{or} quad x = 4

]

Therefore, the values of ( x ) that satisfy the equation ( x^2 + 2x = 24 ) are ( x = 4 ) and ( x = -6 ).