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?

Question

asked May 13, 2019 120k views

2 Answers

Pugsley · Answer 1 · 2019-05-19T18:08:24+0000

Answer:

(2√(2)x-(5)/(√(2)))^(2)=(31)/(2)}

Step by step solution

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

Multiplying each term with
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)}