Question

x-2= square root2x-5 solve equation???

Answer 1

Can you find the square of both sides?

Answer 2

\( \color{Black}{\Rightarrow (x - 2)^2 = \sqrt{2x - 5}^2}\)

Answer 3

Remember:
\((a - b)^2 = a^2 - 2ab + b^2\)

Answer 4

(a-b)^2 = a^2 - 2ab + b^2

Answer 5

2x-5=x^2-4x+4

Answer 6

That's right.
Now add 5 to both sides, then subtract 2x from both.

Answer 7

You'd supposedly have a quadratic equation after doing all that.

Answer 8

Square both sides :)

Answer 9

x^2-6x +9

Answer 10

That's right!
You may use factoring, as that is a perfect square.

Answer 11

Factoring/completing the square.

Answer 12

answer would be (-3,3)

Answer 13

Nope, there's only one root here with a multiplicity of 2(remember how we have an exponent of 2?)

Answer 14

You may express \(x^2 - 6x + 9\) as a perfect square. How'd you do that?

Answer 15

(x-3)(x+3)

Answer 16

Nope. That makes \(x^2 - 9\) when you multiply 'em out.

Answer 17

And that's not a perfect square..

Answer 18

your right.

Answer 19

(x-3)(x-3)

Answer 20

so x=3

Answer 21

Yep, so what's the solution?

Answer 22

x=3

Answer 23

That's correct!