Question

Solve for x. Sqrt8 (Sqrt2 - x) = 11

Answer 1

Answer:$\frac{-7\sqrt{2} }{4}$

Step-by-step explanation:

So first, let's get rid of the parentheses. We can multiply it out to get $\sqrt{16}-x\sqrt{8} =11$. We know that the square root of 16 is ±4, so now our equation is ±4 - $x\sqrt{8}$=11. I'm guessing since the problem only has one solution it's most likely only positive 4, so let's revise our equation to 4 - $x\sqrt{8}$=11. We can use inverse operations to make the a little easier to solve: -7= $x\sqrt{8}$. We divide both sides by $\sqrt{8}$ to get $\frac{-7}{\sqrt{8} } =x$, which we can rationalize (remove the square root from the denominator so that it's a proper answer) by multiplying by $\frac{\sqrt{8} }{\sqrt{8} }$ (which is equal to one so we can use it) which is equal to $\frac{-7\sqrt{8} }{8}$. Let's finish this by simplifying it. $\sqrt{8} =2\sqrt{2}$ (2x$2^{2}$). We can simplify it further by simplifying the 2, making it $\frac{-7\sqrt{2} }{4}$.

Hope this wasn't too confusing! I'll answer any questions.

Answer 2

Answer:

x = -7 sqrt(2)/4

Step-by-step explanation:

Sqrt8 (Sqrt2 - x) = 11

Simplify sqrt(8) = sqrt(4*2) = 2 sqrt(2)

2 sqrt(2) (Sqrt2 - x) = 11

Distribute

2 *2 - 2 sqrt(2) x = 11

4 - 2 sqrt(2)x = 11

Subtract 4 from each side

4-2sqrt(2)x -4 = 11-4

-2 sqrt(2)x = 7

Divide each side by -2 sqrt(2)

-2 sqrt(2)x /-2 sqrt(2) = 7/ -2 sqrt(2)

x = - 7/ 2 sqrt(2)

Multiply top and bottom by sqrt(2)

x = - 7/ 2 sqrt(2)  * sqrt(2)/ sqrt(2)

x = -7 sqrt(2)/4