How do I solve the equation, 2x + 5 * sqrt(x) - 3 = 0, and what is the answer?

Question

I found this equation in a math textbook and did not know how to solve it.

Answer 1

2x + 5√x - 3 = 0

 

2x - 3 = -5√x

 

Square both sides to obtain 4x² - 12x + 9 = 25x

 

4x² - 37x + 9 = 0

 

(4x - 1)(x - 9) = 0

 

x = 1/4 or x = 9

 

Checking these values in the original equation, we see that 9 does not satisfy the equation, but 1/4 does.

 

So, the only solution is 1/4.  

 

 

Answer 2

u = √x

2u² + 5u - 3 = 0

(2u - 1)(u + 3) = 0

 

2u = 1

u = 1/2

√x = 1/2

x = 1/4

 

u = -3

√x = -3     not possilbe

Answer 3

Subtract 2x and add 3 on both sides of the equation.

 

5√(x) = -2x + 3

 

 

Square both sides of the equation to undo the square-root symbol.

 

25x = (-2x + 3)(-2x + 3)

 

25x = 4x² - 12x + 9

 

 

Subtract 25x on both sides of the equation.

 

0 = 4x² - 37x + 9

 

 

You now have a quadratic equation.  Solve for x.  You may need to use the quadratic formula.