use the square root property to solve the equation.(7x-6)^2=2

Question

1. use the square root property to solve the equation.(7x-6)^2=2

 

2. solve for the indicated variable y=kx(4-x) for x

Answer 1

(7x-6)² = 2

 

Take the square root of both sides:

 

      √(7x-6)² = ±√2

 

There are two solutions.

• Solution 1:

         7x - 6 = +√2

         7x =  6 + √2

         x = (6 + √2)/7

• Solution 2:

         7x - 6 = -√2

         7x = 6 - √2

         x = (6-√2)/7

 

Check:

• Solution 1:

         (7x-6)2 = 2

         (7((6 + √2)/7 - 6)² = 2

         (6 + √2 - 7)² = 2

         (√2)² = 2

         2 = 2

         Check!

• Solution 2:

          (7x-6)2 = 2
          (7((6 - √2)/7 - 6)² = 2
          (6 - √2 - 7)² = 2
          (-√2)² = 2
          2 = 2
          Check!