Question 425969
2a^2 + 30a + 100


set it equal to 0


you get:


2a^2 + 30a + 100 = 0


divide both sides of the equation by 2 to get:


a^2 + 15a + 50 = 0


50 can be factored in several ways.


1 * 50
2 * 25
5 * 10


looking at each of these and adding the 2 factors together you get:


1 + 50 = 51
2 + 26 = 26
5 + 10 = 15


factors of 5 and 10 look interesting because 5*10 = 50 and 5+10 = 15.


your factors could very well be:


(a + 5) * (a + 10) = 0


multiply these 2 factors together to get a^2 + 10a + 5a + 50 = 0


combine like terms to get a^2 + 15a + 50 = 0


these are your factors.


to get back to the original equation, multiply both sides of this equation by 2 to get 2a^2 + 30a + 100.


the basic procedure in factoring a quadratic equation is to get the equation into standard form and then to reduce it to the lowest possible common factors.


your expression was 2a^2 + 30a + 100.


place it into standard form by setting it equal to 0 to get:


2a^2 + 30a + 100 = 0


factor out to 2 to reduce it as much as possible to get:


a^2 + 15a + 50 = 0


etc. as we did above.


your factors came out to be (x+5) * (x+10) = 0


this equation is true if (x+5) = 0 or if (x+10) = 0.


(x+5) = 0 if x = -5
(x+10) = 0 if x = -10


your answer is:


x = -5 or x = -10