Rewrite the equation by completing the square. 2x^2 – 3x-5=0 Question Rewrite the equation by completing the square. 2x^2 – 3x-5=0 in progress 0 Math Rylee 2 weeks 2021-10-03T11:15:01+00:00 2021-10-03T11:15:01+00:00 1 Answer 0

## Answers ( )

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]