Question

How do you solve `9x^2 - 7x = 12` using completing the square?

Answer 1

I found:
`x_1=1/18(7+sqrt(481))`
`x_2=1/18(7-sqrt(481))`

Explanation:

Let us do some manipulations:

`9x^2-7x=12` add and subtract `49/36`
`9x^2-7x+49/36-49/36=12`
`9x^2-7x+49/36=12+49/36`
`(3x-7/6)^2=481/36` root square both sides:
`3x-7/6=+-sqrt(481/36)=`
`x=1/3(7/6+-sqrt(481/36))`
`x_1=1/18(7+sqrt(481))`
`x_2=1/18(7-sqrt(481))`