Question

Solve x2 − 12x 5 = 0 using the completing-the-square method.

Answer 1

(x-6)²-6²+5=0
(x-6)²-36+5=0
(x-6)²-31=0
(x-6)²=31
x-6=√31
x=6±√31

x= 11.57 or x=0.43

Answer 2

`x=6+√(31)`

`x=6-√(31)`

Explanation:

Solve
`x^2-12x+5 = 0` using the completing-the-square method.

Subtract 5 from both sides

`x^2-12x=-5`

In completing the square method , we take coefficient of middle term and then divide by 2 and square it

12 divide by 2 is 6

6^2 = 36

Add 36 on both sides

`x^2-12x+36=-5+36`

`x^2-12x+36=31`

Now we factor the left hand side

`(x-6)(x-6)=31`

`(x-6)^2=31`

Take square root on both sides

`x-6=+-√(31)`

Now add 6 on both sides

`x=6+-√(31)`

So there are two values for x

`x=6+√(31)`

`x=6-√(31)`