Question

solve the equation by completing the square..2y^2+9=10y

Answer 1

\[2y ^{2}-10y+9=0\]

Answer 2

okay

Answer 3

still need a hand on this or did you figure it out?

Answer 4

need a hand please

Answer 5

so to complete the square, you have to add some constant value to both sides of the equation such that the equation can be written as (ay+b)^2=c

so start by moving everything to one side of the equation:
\[2y^2-10y+9=0\]
Then I'd recommend dividing everything by 2 to simplify things a bit later on.

then you have to realize that in order to get the equation into (ay+b)^2 form, the expanded form must be in the form a^2y^2+2ayb+b^2

so:
\[y^2-5y+9/2+x=a^2y^2-2aby+b^2\] where x is the constant you will need to add to both sides of the equation.

With this you can see that \[a^2=1 \rightarrow a=1\]

then solve for b next:
\[-5 = -2ab \rightarrow 5/2=b \]
\[b^2=25/4=6.25\]

finally you need your constant value to match up with this b value.

currently you have 2y^2-10y+9=0 and you want b^2 to equal 6.25 or 25/4 to complete the square.

To do this add 7/4 or 1.75 from both sides of the equation
this leaves you with:
\[y^2-5y+25/4=7/4\]

Now this is where it all comes together:
now the equation is in a perfect square form, so it can be written as
\[(y-5/2)^2=7/4\]

Finally you get to solve by taking the square root of each side, then adding 5/2 to each side

Answer 6

So the final answer comes to 7/4?

Answer 7

not quite. y doesnt equal 7/4; (y-2.5)^2=7/4

to solve for y, which is what you wanted to solve for, take the square root of both sides,
so
y-2.5=sqrt(7)/sqrt(4) = sqrt(7)/2

then add 2.5 to each side
to get y=sqrt(7)/2+2.5
or
y=(sqrt(7)+5)/2

unfortunately the problem didn't give the nicest numbers so that's about as clean as the answer's going to get

Answer 8

That has been my problem, the answer it is giving does not make much sense to me. But well, I guess this is it

Answer 9

Thanks for your help