1. ## Solving Quadratic Equations Using The Square Root Principal

I need help with this question: $5/2 = 6/(x+4)^2$ (Rationalize the denominator) Thanks

2. The denominators already are rational.

You can cross multiply then solve the equation. If that's what you want to do?

$\frac{5}{2}=\frac{6}{(x+4)^2}$

$5(x+4)^2=12$

Can you take it from there?

3. Originally Posted by Stroodle

You can cross multiply then solve the equation. If that's what you want to do?

$\frac{5}{2}=\frac{6}{(x+4)^2}$

$5(x+4)^2=12$

Can you take it from there?
Oh Wait I was FOILing $5(x+4)^2$ instead of taking the square root, thanks. So after that i get $5x+20 = 2sqrt3$ subtract 20 and divide by 5 to get $x = (2sqrt3)/5 - 4$ Is that right?

4. $5(x+4)^2=12$

$5(x+4)(x+4)=12$

$5(x^2+8x+16)=12$

$5x^2+40x+68=0$

Now you can either sub these values into the quadratic formula or complete the square to find the values of x.

Do you know how to do this?

5. I would use the quadratic formula but it says solve using the square root principal, is that just isolating x?

6. Oh, sorry I misunderstood. I'm not familiar with the square root principle. But I assume it's:

$5(x+4)^2=12$

$(x+4)^2=\frac{12}{5}$

$x+4=\pm\sqrt{\frac{12}{5}}$

$x=\pm\sqrt{\frac{12}{5}}-4$

7. Yes that is it but you have to rationalize the denominator so would the final answer be $x=2sqrt(15)/5-4?$

8. Originally Posted by Stroodle
Oh, sorry I misunderstood. I'm not familiar with the square root principle. But I assume it's:

$5(x+4)^2=12$

$(x+4)^2=\frac{12}{5}$

$x+4=\pm\sqrt{\frac{12}{5}}$

$x=\pm\sqrt{\frac{12}{5}}-4$
I'd make sure to rationalise the denominator...

$5(x + 4)^2 = 12$

$(x + 4)^2 = \frac{12}{5}$

$x + 4 = \pm\sqrt{\frac{12}{5}}$

$x + 4 = \pm \frac{\sqrt{12}}{\sqrt{5}}$

$x + 4 = \pm \frac{2\sqrt{3}}{\sqrt{5}}$

$x + 4 = \pm \frac{2\sqrt{15}}{5}$

$x = -4 \pm \frac{2\sqrt{15}}{5}$

$x = \frac{-20 \pm \sqrt{15}}{5}$.

This should be the same answer you get if you use the Quadratic Formula...

9. Yep. The answer would be $x=\pm\frac{2\sqrt{15}}{5}-4$

10. Oh yea plus or minus, thanks for your help I really appreciate it.

11. No probs. Finally got there in the end