Wednesday

July 30, 2014

July 30, 2014

Posted by **Algebra** on Wednesday, May 27, 2009 at 9:35am.

3x^(1/2) - x - 6 = 0

how do i do this and solve for x with out just squareing and using quadratic formula. I was never taught the proof of the quadratic formula and would like to know how to do with without squareing and if squaring is the only option which i doubt to solve for x can someone show me the proof using these number step by step

thanks

- Algebra -
**Reiny**, Wednesday, May 27, 2009 at 10:13amyou could try graphing.

change to 3√x = x+6

then split it into

y = 3√x and y = x+6

a few points on the graph would be (0,0), (1,3), (4,6) and (9,9)

the second is of course a straight line with slope of 1 and y-intercept of 6

it is immediately obvious that the two graphs cannot intersect, so your equation has no real solution.

The only other option is to square both sides of 3√x = x+6 ,

to obtain the quadratic equation x^2 + 3x + 36 = 0

which only has complex roots as shown by our graph above.

- Algebra -
**Dr Russ**, Wednesday, May 27, 2009 at 10:16amI am not sure if this helps.

If we rearrange and square each side we end up with

8x^2-12x-36=0

and by inspection we see that one solution is x=3

to find the other divide

8x^2-12x-36 by x-3

which gives

8x-12=0 as the other solution

but check my maths!!

- Algebra -
**Reiny**, Wednesday, May 27, 2009 at 10:23amif you want a "proof" and development of the quadratic equation, it is obtained by completing the square on

Ax + By + C = 0 as shown in

http://mathworld.wolfram.com/QuadraticEquation.html

(BTW, I notice that DrRuss has a small error in his solution.

when you square 3√x you get 9x not 9x^2)

- Algebra -
**Dr Russ**, Friday, May 29, 2009 at 4:53amOOOPS That what comes of solving things quickly!!

**Related Questions**

algebra - factor 3a^2(a-b)-6a(a-b)+21(a-b) Can you show me the steps? I'm just ...

For Hellpp - Algebra 2 - I removed your original post because of an ...

Math-Algebra - Solve: 3x-2y=10 2x+3y=-2 Graph: Substitution: Elimination: Show ...

Algebra 1 - Lately I just have blacked out in my algebra 1 class. Here's a ...

Beginning Algebra - how do i figure out this problem i have to make the equation...

Algebra - Solve: 3x-2y=10 2x+3y=-2 Graph: Substitution: Elimination: Show Your ...

math - in = x out = 2 x so if -1 is in what is out , if 0 in what out, and if 3 ...

Algebra - I can't figure out this problem... 2x-2-(x-1) = 4-1+x-(-3x) solve for ...

algebra - this is probablt really simple, but for some reason I can't find out ...

College Algebra - solve systems of equations by graphing... I get how to graph ...