Question

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

Answer 1

x = -7 sqrt(2)/4

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

Answer 2

Answer:
`(-7√(2) )/(4)`

Explanation:

So first, let's get rid of the parentheses. We can multiply it out to get
`√(16)-x√(8) =11`. We know that the square root of 16 is ±4, so now our equation is ±4 -
`x√(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√(8)`=11. We can use inverse operations to make the a little easier to solve: -7=
`x√(8)`. We divide both sides by
`√(8)` to get
`(-7)/(√(8) ) =x`, which we can rationalize (remove the square root from the denominator so that it's a proper answer) by multiplying by
`(√(8) )/(√(8) )` (which is equal to one so we can use it) which is equal to
`(-7√(8) )/(8)`. Let's finish this by simplifying it.
`√(8) =2√(2)` (2x
`2^(2)`). We can simplify it further by simplifying the 2, making it
`(-7√(2) )/(4)`.

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