Please show work and indicate "answer", using the quadratic formula -

(x+2) (2x+3) = 6


I am tutoring my grandson in High School level Algebra II and it has been a number of years since I've done the quadratic formula, please help.

thank you.

Miriam

Miriam,

The quadratic formula says that if you have the quadratic equation

a x² + b x + c = 0

then you can find x by

For the problem that you sent the first task is to convert the equation into the form

a x² + b x + c = 0

Your equation is

(x+2) (2x+3) = 6

First expand the left side to get

2 x² + 7 x + 6 = 6

and the add -6 to both sides to make the right side zero.

2 x² + 7 x = 0

This is now of the correct form

a x² + b x + c = 0

with a = 2, b = 7 and c = 0. Thus the general quadratic expression gives

and thus x = 0 or x = ^-14/₄ = ^-7/₂ 

However, no one would ever use the general quadratic expression to solve

2 x² + 7 x = 0

This expression factors to yield

2 x² + 7 x = x(2x + 7) = 0

and hence x = 0 or x = ^-7/₂ 

Penny