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

2 Answers
Nov 5, 2017

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

Nov 5, 2017

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