Question

Find the solution set of the quadratic equation by completing the square

2x^2-8x-5=0

Answer 1

The equation 2x^2 - 8x - 5  =  0

Separate variables and constants aside by adding 5 to each side.

2x^2 - 8x - 5 + 5  =  0 + 5

2x^2 - 8x  =  5

Here x^2 coefficient is 6 , for perfect square make x^2 coefficient 1 by dividing each side by 2

x^2 - 4x  =  5/2

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

x^2 - 4x + 2^2  =  5/2 + 2^2

x^2 - 4x + 2^2  =  5/2 + 4

(x - 2)^2  =  (5 + 8)/2

(x - 2)^2  =  13/2

Take square root on both sides.

(x - 2)   =   ± √(13/2)

(x - 2)   =   ± √(26/4)

(x - 2)   =   ± √(26) / 2

x   =  2  ± √(26) / 2

x   =  [ 4  ± √(26) ] / 2

Solutions are x   =  [ 4  + √(26) ] / 2 and x   =  [ 4  - √(26) ] / 2

Answer :

Solutions are x   =  [ 4  + √(26) ] / 2 and x   =  [ 4  - √(26) ] / 2.