Solve x2 3x 10 0 x Simplify your answer Type each soluti

Solve x^2 + 3x - 10 = 0 x = (Simplify your answer. Type each solution only once. Use a comma to separate answers as needed)

x^2 + 3x - 10 = 0

This is a quadratic with a = 1 , b = 3 and c = -10

Lets see if we can factorize this and solve....

The rule for factorizing quadratics is to split the middle term into terms such that :

a) sum of those 2 terms = b = 3 here
b) product of those terms = ac = 1(-10) = -10 here

So,

sum = 3 and product = -10

Trial and error give sus that 5 and -2 work out...

So, we split it as :

x^2 + 5x - 2x - 10 = 0

Now, factor by grouping :
x(x + 5) - 2(x + 5) = 0

Now, take the (x + 5) common :
(x - 2)(x + 5) = 0

By zero factor property :
x - 2 = 0 , x + 5 = 0

So, we get :

x = -5 , 2 -----> ANSWER