Originally Posted by

**unstopabl3** a)

12x^2+x-6

12(x^2+x/12)-6

12{(x+1/24)^2+(1/24)(-1/24)}-6

12{(x+1/24)^2-1/576}-6

[tex]{12(x+1/24)^2+12(-1/576)}-6

{12(x+1/24)^2-1/48}-6

{12(x+1/24)^2-1/48-6(48/48)}

{12(x+1/24)^2-289/48}

**12((x+1/24)^2-289/576)**

12((x+1/24)^2-(17/24)^2) <<<<<<<<< difference of squares!

12(x+1/24+17/24)(x+1/24-17/24))

12(x+3/4)(x-2/3) <<<<<<<<< now split the factor 12 into 3 * 4 and put them into the appropriate bracket

(4x+3)(3x-2)

b)

4+6x=-x^2 **<<<<<<<<< according to the wording of the problem**

x^2+6x+4 = 0

(x^2+6x+9-9)+4=0

(x+3)^2-5=0

(x+3)^2-(sqrt(5))^2=0 **<<<<<<<<<<< difference of squares**

**Factor the difference.**

Aproduct equals zero if one factor equals zero.

Solve each equation for x.

Thanks!