Question

I need to solve x^2+4x-14=0 and I know that using the quadratic formula the answer is -2+-3sqrt(2), but for some reason when I solve it i get -2+-3sqrt(8).
I get the 8 because when I'm at (-4+-sqrt(72))/2, i do 9 * 8 which is 72 and the square root of 9 is 3 so I just leave the 8. What am I doing wrong?

Answer 1

check the value inside the square root its

\[x = \frac{-4\pm \sqrt{4^2 - 4 \times 1 \times (-14)}}{2 \times 1}\]

so this simplifies to

\[x = \frac{-4 \pm \sqrt{72}}{2} = \frac{-4 \pm \sqrt{36} \times \sqrt{2}}{2}\]

and simplify this

Answer 2

thanks! that helped me get the answer. so should i always choose the greatest numbers that make up 72?

Answer 3

**
when I solve it i get -2+-3sqrt(8).
**
you mean you get
\[ \frac{-4 \pm 3\sqrt{8}}{2} \]
which is correct. But notice that 8 is 2*2*2 so you can continue
\[ \frac{-4 \pm 3\sqrt{2\cdot 2\cdot 2}}{2} \\
= \frac{-4 \pm 3\cdot 2\sqrt{2}}{2} \]
now both terms can be divided by 2, and you get
\[ -2 \pm 3 \sqrt{2} \]

one way to simplify sqr(72) to its simplest is to factor it into its prime factors
2*2*2*3*3
and "pull out" from the square root any "pairs"
i.e.
\[ \sqrt{ 2\cdot 2 \cdot 2 \cdot 3 \cdot 3} = 2\cdot 3 \sqrt{2}\]

Answer 4

thanks!