SOLUTION: I have to find all real solutions for the following equation: {{{(x^2)sqrt(x+3)=(x+3)^(3/2)}}} I converted the {{{sqrt(x+3)}}} into {{{x^(1/2)+3^(1/2)}}} So the equation turned i

Question 352106: I have to find all real solutions for the following equation:
I converted the into
So the equation turned into:

Then I distributed x^2 on one side and ^3/2 on the other. So I get:

The x and 3x can simplify to 4x. and I move this over into the other side.

I feel like I can somehow turn this into a quadratic formula, but unsure how.
So here is where I'm stuck.
Thank you!
-Kayte
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(x^2)sqrt(x+3)=(x+3)^(3/2)
----
Divide both sides by sqrt(x+3) to get:
x^2 = (x+3)
---
x^2-x-3 = 0
---
x = [1 +- sqrt(1-4(-3)]/2
---
x = [1 +- sqrt(13)]/2
============================
Cheers,
Stan H.
RELATED QUESTIONS
Find the real solutions of the equation. (5x^2 - 6)^(1/4) = x I found x to be... (answered by Theo,MathTherapy)

Find the real solutions of each equation. Please help me solve this equation... (answered by Fombitz)

How would I solve this? Find all real solutions of each equation. Please help me... (answered by Alan3354)

Hello, my question is; Find all real numbers X that satisfy the equation... (answered by MathLover1)

Find the real solutions by factoring. x^2 + sqrt{3}x^2 - 3 = 0 Let x^4 =... (answered by ikleyn)

Hi. May I have some help finding solutions to the equation? Find all real solutions of (answered by Edwin McCravy)

Let x(1) and x(2) be the real solutions to the equation x^2-sqrt(11)x+2=0 Then the... (answered by stanbon)

Find all real solutions of the equation.... (answered by josgarithmetic)

I am to find all the zeros of the equation. -x^3 + x^2 -3x + 3 = 0 I need to write... (answered by nerdybill)