Question

the equation -2x^2+3=-9x is rewritten in the form of -2(x-p)^2 +q=0. What is the value of q?the equation -2x^2+3=-9x is rewritten in the form of -2(x-p)^2 +q=0. What is the value of q?

Answer 1

Value of q is
`(105)/(8)` .

Explanation:

We have , the equation
`-2x^2+3=-9x` is rewritten in the form of
`-2(x-p)^2 +q=0` . We need to find What is the value of q . Let's find out:

Let's simplify equation
`-2x^2+3=-9x` into
`-2(x-p)^2 +q=0` :

⇒
`-2x^2+3=-9x`

⇒
`-2x^2+9x+3=0`

⇒
`2x^2-9x=3`

⇒
`2(x^2-(9)/(2)x)=3`

⇒
`(x^2-(9)/(2)x)=(3)/(2)`

⇒
`(x^2-2(1)(9)/(4)x)=(3)/(2)`

⇒
`(x^2-2(1)(9)/(4)x) + ((9)/(4))^2=(3)/(2) + ((9)/(4))^2`

⇒
`(x-(9)/(4))^2=(3)/(2) + ((81)/(16))`

⇒
`(x-(9)/(4))^2=(24)/(16) + ((81)/(16))`

⇒
`(x-(9)/(4))^2=(105)/(16)`

⇒
`-2(x-(9)/(4))^2=-2((105)/(16))`

⇒
`-2(x-(9)/(4))^2=-(105)/(8)`

⇒
`-2(x-(9)/(4))^2+(105)/(8) = 0`

Comparing this equation to
`-2(x-p)^2 +q=0` ,
`q =(105)/(8)` .

Therefore ,Value of q is
`(105)/(8)` .