Question

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

Answer 1

hi my litler friend

$(x-5)^2=3\\(x-5)=+-\sqrt{3} \\\\x-5=\sqrt{3} \\x=5+\sqrt{3} \\\\x-5=-\sqrt{3} \\x=5-\sqrt{3} \\\\\\S=(5-\sqrt{3},5+\sqrt{3})$

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

Answer 2

Answer:

Exact solutions: $x = 5+\sqrt{3} \ \text{ or } \ x = 5-\sqrt{3}$

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

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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.

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

Use a calculator for the last step.