Question

Joseph has started completing the square on the equation 3x^2-7x+12=0. He has worked to the point where he has the expression x^2 - 7/4 x =-4. Use complete sentences to describe joesphs steps up to this point and whetger or not his work is accurate

Answer 1

Starting with 3x^2-7x+12=0, we divide all four terms by 3, resulting in the following factored form:

3(x^2-[7/3]x+4)=0.

Since 3 cannot equal 0, we can focus on the following:

x^2 - 7/4 x =-4

This completes the assignment (describe Joe's steps up to this point).



If you wish to go further:

Next, take HALF of the coefficient of x and square your result:

(-7/[4][2])^2 = 49/64

Add this to both sides of x^2 - 7/4 x =-4:    x^2 - 7/4x + 49/64 =-4+49/64

Rewrite the left side as (x-7/8)^2 and the right side as 49/64 - 256/64

Simplify the right side by combining these terms:  -207/64

Then x-7/8 = plus or minus (1/8)sqrt(-207)

Next, x = 7/8 plus or minus (1/8)*i*√207, or

          7 plus or minus i*√207
 x = ----------------------------------
                         8