Answer:
x = 1 and -2
Step-by-step explanation
Given the expression
2x^2 + 2x - 4 = 0
We are to find the zero of the equation using the completing the square method
Step 1: Divide through by 2
2x^2/2 + 2x/2 - 4/2 = 0/2
x^2 + x - 2 = 0
Step 2: Add 2 to both sides of the equation
x^2 + x - 2 + 2 = 0+2
x^2 + x = 2
Step 3: Complete the square by adding the square of half of coefficient of x to both sides as shown
Coefficient of x is 1
Half of 1 = 1/2
Square of 1/2 = (1/2)^2 = 1/4
Add 1/4 to both sides
x^2 + x + (1/2)^2= 2 + 1/4
(x+1/2)^2 = 9/4
Sqare root both sides
x + 1/2 = \sqrt[9/4]
x + 1/2 = 3/2
x = 3/2 - 1/2 and -3/2 - 1/2
x = 2/2 and -4/2
x = 1 and -2