solve 2(x-8)^2=20 by using square roots. I got positive and negative 3.74. Is that correct?

Question

I'm currently in Algebra B at my school and I'm having trouble with this one problem. Help!!

Answer 1

Hi Kendall, the first step you need to take is to divide both sides by 2.

2(x-8)²⁼20

   2        2

Simplify,

            (x-8)²=10 , Now apply square root in both sides of the equation.

     

          √(x-8)²=√10, having 

     

               x-8 = ±√10  , Next step is to separate into two equations, one positive and one negative

 

    x-8=+√10  and x-8 = -√10     Solving both equations we have (in this case approximate √10 to 3.16

 

     x = 3.16+8 and x = -3.16 + 8

 

     x = 11.16    and x = 4.84

 

so the solutions are {4.84, 11.16}

 

I hope this help you!

 

Sincerely

 

Henry 

 

 

Answer 2

Hy Kendall,

 

 

 

Divide by 2 on both sides.

 

(x -8)^2 = 10

 

Take the square root on both sides.

 

 

(x -8) = √10

 

( x -8 )= 3.16 and (x - 8) = -3.16

 

x = 11.16 and x = 4.84

 

 

I hope you can understand the steps and how I solved this problem. 

 

Good luck with all of your problems.

 

 

 

regards,

 

Mayuran