Question

Brian is solving the equation 2x-3/4x=5 What value must be added to both sides of the equation to make the left side a perfect-square trinomial?

Answer 1

yess u bring to 2 as a fraction then put 5 above a x

Answer 2

`(2√(2)x-(5)/(√(2)))^(2)=(31)/(2)}`

Step by step solution

`2x-(3)/(4x)=5`

Multiplying each term with
`4x` we get

`2x*4x-3=5*4x`

`8x^2-3=20x`

`8x^2-20x-3=0`

Splitting the above expression in the form of

`a^2-2*a*b+b^2`

where
`a=2√(2)`

`((2√(2)*x)^(2))-2*(2√(2))*((5)/(√(2)))-3`

adding and subtracting

`((5)/(√(2)))^(2)`

to the above polynomial..

`(2√(2)*x)^(2)-2*2√(2)*((5)/(√(2)))+((5)/(√(2)))^(2)-((5)/(√(2)))^(2)-3=0`

`(2√(2)*x)^(2)-2*2√(2)*((5)/(√(2)))+((5)/(√(2)))^(2)-(25)/(2)-3=0`

`(2√(2)*x-(5)/(√(2)))^(2)-(25+6)/(2)}=0`

`(2√(2)x-(5)/(√(2)))^(2)=(31)/(2)}`