Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary. ​x2 – 5x = 12

Answer 1

x^2 - 5x = 12
x^2 - 5x + 6.25 = 12 + 6.25
(x - 2.5)^2 = 18.25
x - 2.5 = (+-) sqrt 18.25
x = 2.5 (+ - ) 4.27

x = 2.5 + 4.27 = 6.77 <==
x = 2.5 - 4.27 = -1.77 <==

Answer 2

`x=6.77` and
`x=-1.77`

Explanation:

The given equation is:

`x^2-5x=12`

Adding
`6.25` on both sides of the above equation, we get

⇒
`x^2-5x+6.25=12+6.25`

⇒
`(x-2.5)^2=18.25`

⇒
`(x-2.5)={\pm}{√(18.25)`

⇒
`(x-2.5)={\pm}4.27`

⇒
`(x-2.5)=4.27` and
`(x-2.5)=-4.27`

⇒
`x=4.27+2.5` and
`x=-4.27+2.5`

⇒
`x=6.77` and
`x=-1.77`

which is the required values of x.