The area of a parallelogram is given by the equation 2(x)^2+7x-3=0, where x is the length of the base. Find: (a) The equation of the parallelogram in the form a(x+m)^2+n=0. (b) The value of x.

(a)STEP 1: Take out the coefficient of x^2 from the x^2 and x terms.
2(x)²+7x-3=0 2(x²+(7/2)x)-3=0
STEP 2: Complete the Square by finding (b/2)².
(b/2)².= (7/4)²Therefore, 2[(x+(7/4))²-(7/4)²]-3=0
STEP 3: Expand and Simplify.
2[(x+(7/4))²-(49/16)]-3=0 2(x+(7/4))²-(49/8) -3=0 2(x+(7/4))²-(73/8)=0
(b) 2(x+(7/4))² =(73/8) (x+(7/4))²=(73/16) x=(-7/4)+(73/16)^(1/2)or (-7/4)-(73/16)^(1/2) x=0.386 or -3.886
However as x is the value of a length, x>0.
Therefore, x=0.386.