How would I solve this?

x^2+10x+24=0

you want two factors of 24 which add up to 10. List the factors:

1 2 3 4 6 8 12 24

Take them in pairs, working in from the ends. Note that 4 and 6 add up to 10, so you have

(x+4)(x+6) = 0
x = -4 or -6

oh okay thank you, do i plug them in now or leave it at that?

oh wait, nvm

To solve the quadratic equation x^2 + 10x + 24 = 0, you can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the following formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, the equation is x^2 + 10x + 24 = 0, which means a = 1, b = 10, and c = 24. Plugging these values into the quadratic formula, we get:

x = (-(10) ± √((10)^2 - 4(1)(24))) / (2(1))

Simplifying further:

x = (-10 ± √(100 - 96)) / 2

x = (-10 ± √4) / 2

Now, let's compute both solutions:

x1 = (-10 + √4) / 2

Simplifying:

x1 = (-10 + 2) / 2

x1 = -8 / 2

x1 = -4

x2 = (-10 - √4) / 2

Simplifying:

x2 = (-10 - 2) / 2

x2 = -12 / 2

x2 = -6

Therefore, the solutions to the quadratic equation x^2 + 10x + 24 = 0 are x = -4 and x = -6.