Question

Solve the equation: (√x-1)=x-7

Answer 1

(√x-1) = x - 7
square both sides
x-1 = (x-7)^2
can you do it from here?

Answer 2

When you square the square root it turns into an absolute value, right?

Answer 3

when you square a number in a square root symbol
\[\huge (\sqrt{x})^2 = x\] you get that number inside the square root symbol

Answer 4

and I would factor out the (x-7)^2?

Answer 5

yes, multiply (x-7)(x-7)

Answer 6

Now I have: x-1=x^2-14x+49, am I suppose to add the 1 to both sides?

Answer 7

You arrange it so that 0= something.
So you add one to both sides and also
subract x from both sides.

Answer 8

You were right to be wary of the squaring operation though.
You will get 2 solutions when you factor, only one of them actually satisfies the original equation.

Answer 9

Once I minus the x from both sides and add the one, it looks like: 0=x^2-13x+50, right?

Answer 10

-14x -x=-15x

Answer 11

0=x^2-15x+50

Answer 12

Yeah that's right, I didn't notice that I did that.

Answer 13

So now we have to factor that. :)

Answer 14

How come the x=5 doesn't satisfy the equation?

Answer 15

Because of the squaring we did to get rid of the radical.

Answer 16

The easiest way to solve these though is just how we did it, and then know that you have to check your answers to see which actually work.

Answer 17

Oh ok I see what you mean. Thank you for your help!

Answer 18

No problem :)