Question

How do you solve `25x ^ { 2} + 50x = 24`?

Answer 1

`x=2/5, -12/5`

Explanation:

You can either use the quadratic formula or simply factor

Using factoring,
`25x^2 + 50x - 24=0`
`(5x-2)(5x+12)=0`

Therefore,
`5x-2=0`
`x=2/5`

`5x+12=0`
`x=-12/5`

Using quadratic formula,
`x= (-b +- sqrt(b^2-4ac) )/ (2a)`

`a=25 , b=50 , c=-24`

`x= (-50 +- sqrt(50^2-(4*25*-24)) )/ (2*25)`

`x= (-50 +- 70) / (50)`

`x= (-50 + 70) / (50)`
`x=2/5`

`x= (-50 - 70) / (50)`
`x=-12/5`

Answer 2

`x=2/5color(white)("xxx")"or"color(white)("xxx")x=-2 2/5`

Explanation:

Given
`color(white)("XXX")25x^2+50x=24`

`25(x^2+2x)=24`

`color(green)(25)(x^2+2xcolor(magenta)(+1))=24color(magenta)(+1)xxcolor(green)(25)`

`25(x+1)^2=49`

`(x+1)^2=49/25`

`(x+1)=+-7/5`

`x=+7/5-1=2/5color(white)("xxx")"or"color(white)("xxx")x=-7/5-1=-12/5=-2 2/5`