How do you solve #5x ^ { 2} + 9x - 20= 4- 5x#?

1 Answer
May 30, 2018

Answer:

Rearrange the expression so one side equals zero, then use the quadratic formula to find #x={-4,1.2}#

Explanation:

First, we'll rearrange the expression so the Right Hand Side (RHS) equals zero. This will give us our quadratic expression to use in the quadratic formula:

#5x^2+9x-20color(red)(-4)color(blue)(+5x)=cancel(4)color(red)(cancel(-4))cancel(-5x)color(blue)(cancel(+5x))#

#5x^2+9xcolor(blue)(+5x)-20color(red)(-4)=0#

#5x^2+14x-24=0#

Now, we'll utilize The Quadratic Formula. For any quadratic expression that looks like #ax^2+bx+c#:

#x=(-b+-sqrt(b^2-4ac))/(2a)#

For this case:

#a=5#
#b=14#
#c=-24#

Let's plug that in:

#x=(-14+-sqrt((14^2)-4(5)(-24)))/(2(5))#

#x=(-14+-sqrt(196-4(-120)))/10#

#x=(-14+-sqrt(196+480))/10#

#x=(-14+-sqrt(676))/10#

#x=(-14+-26)/10#

#x={(-14-26)/10,(-14+26)/10}#

#x={(-40)/10,12/10}#

#color(green)(x={-4,1.2})#