posted by Algebra

can show me how to do this with out just squaring

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


  1. Reiny

    you 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.

  2. Dr Russ

    I am not sure if this helps.

    If we rearrange and square each side we end up with


    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!!

  3. Reiny

    if 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

    (BTW, I notice that DrRuss has a small error in his solution.
    when you square 3√x you get 9x not 9x^2)

  4. Dr Russ

    OOOPS That what comes of solving things quickly!!

Respond to this Question

First Name

Your Answer

Similar Questions

  1. math,algebra

    can someone help me out factor out this 0=16t^2-122t+180 i have so far this but the last one i am not sure 8(2t^2-14t + ?
  2. Help With Math

    Using the quadratic formula to solve equations. -12^2 + 12 x-9 = -7x^2 10x^2 + 5x + 12 = 0 6x^2 + 12x = - 1 11x^2 - 7x -1 = 0 2x^2 -18x + 16 = 0 Can u show work to help me out
  3. 8th Grade Algebra

    You know how to solve quadratic equations using algebra, graphs and the quadratic formula. Sometimes one method of solving is more convenient than another method. Describe how you would solve each equation. Give reasons for you answers. …
  4. algebra II

    I'm quite clueless as to how to solve this. I know the quadratic equation but am not sure how to get this equation into the format to plug in to the quadratic... Solve the quadratic equation using the formula [1/(1+x)]-[1/(3-x)]=(6/35) …
  5. College Math II

    Solve by using the quadratic formula. x^2 + 6x + 6 = 0 I am having problems using the quadratic formula to get the right answer. Can someone show me the steps that I use?
  6. math (cant figure it out)

    How to find the surface area of a cylinder with a diameter of 6ft and a height of 20cm using 3.14 rounded to the nearest whole number. (I cant figure it out my book doesn't give an example of it just a radius formula and ive tried …
  7. Calculus II

    So I have Maclaurin series for sinx = ∑(-1)^n[x^(2n+1)]/(2n+1)!. I need to write out new series for sin(x^2). This will be equivalent to squaring the whole Maclaurin series of sinx, right?
  8. Quadratic Functions2

    Determine the standard form of a quadratic function whose graph has a y intercept of 8 and a vertex at (-2,-4). The answer is f(x)= 3x^2 + 12x +8 but I can't figure out how to get the answer. Solve x^2 + x=6, by factoring. The answer …
  9. Ap algebra

    2+3X^2-X^3=0 by use quadratic formula. The answer of textbook is 3.19 So I solved and came out a wrong answer What I did factor out (-X+3)X^2+2=0 Then By quadratic formula, a=1,b=0,c=2. Thus I got sqrt(8)/2
  10. Algebra

    I just need to confirm an answer I got when trying this out myself. I'm not too confident so I would appreciate it if someone could tell me if this is correct before I turn it in?

More Similar Questions