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)