2. Square root of x-2 (+x which isn't under square root.) = 8?

Question

Can you walk me through the steps?

Answer 1

sqrt (x-2) + x = 8
sqrt(x-2) = 8 - x
square the equation
x - 2 = 64 + x^2 - 16x
x^2 - 17x + 66 = 0
x^2 - 6x - 11x + 66 = 0
x(x-6) - 11(x-6) = 0
(x-11)(x-6)=0
ie, x = 6, 11

As you are taking sqrt of (x-2) it can be taken as + or minus, with x=6 you have to take (+) sign.. and with x=11 you have to take (-) sign.

Answer 2

sqrt(x - 2) + x = 8,
what you want to do is to get rid of the sqrt right? you could square both sides, but that doesn't get rid of the sqrt, so move x to the other side, -x for both
sqrt(x-2) = 8 - x, now square both sides
x - 2 = 64 - 16x +x^2 now move everything to one side so its set equal to 0

0 = 66 - 17x +x^2, i highly doubt you can easily solve this so lets use the quadratic formula which will be
x = ([-b (+/-) sqrt ( (b)^2 - 4*a*c) ] / [2 * a])
from ax^2 + bx + c = 0
x = ([17 (+/-) sqrt ( (-17)^2 - 4*66 *1) ] / [2 * 1])

edit: on second look, you can easily find two values for x
0 = 66 - 17x +x^2
0 = (x - 11)(x - 6)

and x = 11, 6

Answer 3

the answer given by jas is correct.

A couple of things to mention...at the beginning of a problem like this you always want to isolate your square root...that's why he subtracted the x to the other side.

Second, I want to make sure you understand why you ignore one answer...whenever you "square both sides" as he said in his steps, you lose information (because any time you square anything you only get a positive response...and it can be deceiving). So, whenever you are solving a problem involving "squaring both sides" be sure to go back to the original problem and plug in both solutions. You may find you have one that doesn't work...in this case the 11.

Answer 4

If I read your question right, it should be like this...

(x-2)^2 + x = 8

Subtract 8 from both sides.

(x-2)^2 + x - 8 = 0

Factor out the (x-2)^2, which will be, x^2 - 4x + 4

Plug that into the equation, then simplify and distribute the variables.

x^2 - 4x + 4 + x - 8 = 0

x^2 - 3x - 4 = 0

Factor that...

(x+1)(x-4) = 0

x = -1 or 4

If you don't know how to factor, search it on internet.

Answer 5

if by this you mean

sqrt(x - 2) + x = 8
sqrt(x - 2) = 8 - x
square both sides
x - 2 = (8 - x)^2
x - 2 = (8 - x)(8 - x)
x - 2 = 64 - 8x - 8x + x^2
x - 2 = 64 - 16x + x^2
x^2 - 17x + 66 = 0
(x - 11)(x - 6) = 0
x = 11 or 6

Answer 6

sqrt(x-2) + x = 8.

Hmm...

WE can't figure this out by any conventional method. And guess and check is to confusing. So we give up.

BTW the answer is 6

Oops... I forgot the method where you square both sides...

Jas is right.

Answer 7

(Sq x-2)+x=8
(Sq x-2)=8-x
x-2=x^2-16x+64 (squaring both sides)
x^2-17x+66=0
x^2-11x-6x+66=0
x(x-11)-6(x-11)=0
(x-6)(x-11)=0
x=6,x=11(ignored)
so the ans=6

Answer 8

sqrt(x-2) + x = 8
sqrt(x-2) = 8 - x
(x-2) = 64 - 16x + x^2
0 = 66 - 17x + x^2

Then use quadractic formula:

x = [-b +/- sqrt(b^2 - 4ac)] / 2a

where:
a = 1
b = -17
c = 66

Answer 9

[EDIT] oops I went wrong. Yeah what Jas said is right.

Answer 10

Are you sure you arent in summer school?