Solve for x in the equation 2x^2-4x-9=29

x = 1  ±2sqrt(5)

Step-by-step explanation:

2x^2-4x-9=29

Add 9 to each each side

2x^2-4x-9+9=29+9

2x^2-4x=38

Divide by 2

2/2x^2-4/2x=38/8

x^2 -2x =19

Complete the square

x^2 -2x + (-2/2)^2 = 19 +(-2/2)^2

x^2 -2x +1 = 19+1

(x-1)^1=2 = 20

Take the square root of each side

sqrt((x-1)^2) = ±sqrt(20)

x-1 =  ±sqrt(20)

Add 1 to each side

x-1+1 = 1  ±sqrt(20)

x = 1 ±sqrt(20)

Simplifying the square root of 20

x = 1  ±sqrt(4)sqrt(5)

x = 1  ±2sqrt(5)