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.
MA
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