What are the solutions to this equation x^2+3x=10

To find the solutions, subtract 10 from both sides so that the equation is equal to zero: x^2 + 3x - 10 = 0

Now, find two numbers that multiply together to get -10, but add to get 3.

These two numbers would be 5 and -2.

We rewrite the equation like this: x^2 + 5x - 2x - 10

Put them into two separate problems:

(x^2 + 5x) and (-2x - 10)

Factor them:

x(x + 5) and -2(x + 5)

Both of them have (x+5) in common, so we can rewrite this problem as

(x-2)(x+5) = 0

We now have (x-2) = 0 and (x+5) = 0

The solutions are 2 and -5