Solving the following quadratic equation by the method of co

Solving the following quadratic equation by the method of completing the square simplify where possible Solve the following radical equation. Make you test your results. Simplify where possible. squareroot 2x +1 - squareroot x - 1 Solve the following rational equation. List all restrictions on the variable. x/x - 5 + 5/x = 11/6

Solution

1) 3x^2 -8x = -2

By compltion of sqauare

3(x^2 -8x/3) =-2

3(x^2 - 8x/3 +16/9 -16/9) =-2

3(x -4/3)^2 -16/3 = -2

3(x- 4/3)^2 = -2 +16/3

(x-4/3)^2 = 10/9

take square root on both sides:

x- 4/3 = + /- sqrt(10)/3

x = 4/3 + / - sqrt(10)/3

2) x/(x-5) +5/x = 11/6

[ x^2 +5(x-5) ]/(x(x-5) = 11/6

[ x^2 +5x - 25 ]6 = 11x^2 - 55x

6x^2 +30x - 150 = 11x^2 -55x

5x^2 - 85x +150 =0

x^2 - 17x +30 =0

solve the quadratice using quadartic root formula:

x = ( 17 +/- sqrt(17^2 - 4*30) )/2

=15 , 2

x= 15 , 2 (solution)