# How do you solve #2x - 9\sqrt { x } + 4= 0#?

##### 2 Answers

Aug 24, 2017

See below.

#### Explanation:

Move the term with the radical to the right hand side:

square both sides and collect like terms:

collect and equate to 0:

Factor:

solution:

Aug 24, 2017

#### Explanation:

Given:

#2x-9sqrt(x)+4 = 0#

Let

#0 = 8(2x-9sqrt(x)+4)#

#color(white)(0) = 8(2t^2-9t+4)#

#color(white)(0) = 16t^2-72t+32#

#color(white)(0) = (4t)^2-2(4t)(9)+9^2-49#

#color(white)(0) = (4t-9)^2-7^2#

#color(white)(0) = ((4t-9)-7)((4t-9)+7)#

#color(white)(0) = (4t-16)(4t-2)#

#color(white)(0) = 8(t-4)(2t-1)#

So:

#t=4" "# or#" "t=1/2#

Then:

#x = t^2 = 4^2 = 16" "# or#" "x = t^2 = (1/2)^2 = 1/4#