Question

Solve (x-5)^2=3 question has to be 23 characters so I'm typing this lol

Answer 1

Exact solutions:
`x = 5+√(3) \ \text{ or } \ x = 5-√(3)`

Approximate solutions:
`x \approx 6.732051 \ \text{ or } \ x \approx 3.267949`

==================================================

Work Shown:

Apply the square root to both sides, then add 5 to both sides

Don't forget about the plus/minus so you can get two solutions.

`(x-5)^2 = 3\\\\√((x-5)^2) = √(3)\\\\|x-5| = √(3)\\\\x-5 = \pm√(3)\\\\x-5+5 = \pm√(3)+5\\\\x = 5\pm√(3)\\\\x = 5+√(3) \ \text{ or } \ x = 5-√(3)\\\\x \approx 6.732051 \ \text{ or } \ x \approx 3.267949\\\\`

Use a calculator for the last step.

Answer 2

hi my litler friend

`(x-5)^2=3\\(x-5)=+-√(3) \\\\x-5=√(3) \\x=5+√(3) \\\\x-5=-√(3) \\x=5-√(3) \\\\\\S=(5-√(3),5+√(3))\\`

if in doubt, let me know. I really like to help.