Answer:
2[(x - 3/4)^2 - 49/16]
Step-by-step explanation:
Factor 2x^2 - 3x-5=0 as follows:
2x^2 - 3x-5=0 = 2(x^2 - (3/2) - 5/2)
Now focus on x^2 - (3/2)x - 5/2 alone.
To complete the square, take half of the coeficient of x: (1/2)(-3/2, or
-3/4. Now square this, obtaining 9/16.
Going back to x^2 - (3/2)x - 5/2, add in 9/16 and then subtract 9/16:
x^2 - (3/2)x + 9/16 - 9/16 -5/2
Rewrite x^2 - (3/2)x + 9/16 as the square of a binomial: (x - 3/4)^2
Then we have: (x - 3/4)^2 - 9/16 - 5/2, or
(x - 3/4)^2 - 9/16 - 40/16, or
(x - 3/4)^2 - 49/16
Now go back to the original equation, 2x^2 - 3x-5=0, recall that this is equivalent to 2(x^2 - (3/2) - 5/2) . Replace x^2 - (3/2) - 5/2) with
(x - 3/4)^2 - 49/16, obtaining 2[(x - 3/4)^2 - 49/16]
