Explain in words how you would complete the square on x2 16

Explain in words how you would complete the square on x² - 16x = 4.

Solution

We will do following steps :-

1. First of all we see that whether the coefficient of x^2 is 1 or not. In our case it is 1 so there is no need to do with this.

2. Take half of the coefficient of the middle term (x- term) i.e -16 , square it and then add both sides of the equation. It means we need to add (-8)^2 = 64 to both sides, we get

x^2 -16x +64 = 4+64

=> x^2 -16x +64 = 68

3. Factor the perfect square trinomial as (x+b/2)^2 i.e. (x-8)^2

(x-8)^2 = 68

4. Take the square root of each side and solve. We never forget to include plus minus sign with the solution.

x-8 = + - sqrt(68)

=> x-8 = + - 2 sqrt (17

=> x-8 = 2 sqrt(17)

=> x = 8 +2sqrt(17)

=> x= 2(4+sqrt(17)

and

x-8 = - 2 sqrt17

=> x= 8 -2sqrt17

=> x = 2 (4- sqrt17)

Hence solutions are x= 2(4+sqrt(17) , 2 (4- sqrt17)