Question

How do you solve `9x ^ { 2} - 70x + 49= 0`?

Answer 1

`9x^2-70x+49 =0`

`x = 7/9 or x = 7`

Explanation:

To solve a quadratic equation there are three algebraic methods you can use:

• factorise
• completing the square
• quadratic formula

To factorise `" "9x^2-70x+49 =0`

`rarr` find factors of `9 and 49` whose products add to `70`

`" "9" and "49`
`" "darrcolor(white)(xxxxx)darr`
`" "9color(white)(xxxxxx)7" "rarr 1 xx7 =7`
`" "1color(white)(xxxxxx)7" "rarr 9xx7 =ul(63)`
`color(white)(xxxxxxxxxxxxxxxxxxxxx)70`

The signs in the brackets will be the same (because of the `+49`)
They will both be negative. (because of the `-70x`)

`:.(9x-7)(x-7)=0`

Set each factor equal to `0` and solve.

`9x-7= 0" " rarr" " x = 7/9`

`x-7=0" " rarr" "x= 7`