How do you solve #x(1-x)+2x-4=8x-24-x^2#?

1 Answer
Jan 6, 2017

Answer:

See full process in the Explanation

Explanation:

First step is to expand the terms within the parenthesis:

#x(1 - x) + 2x - 4 = 8x - 24 - x^2#

#x - x^2 + 2x - 4 = 8x - 24 - x^2#

We can now group and combine like terms:

#x + 2x - x^2 - 4 = 8x - 24 - x^2#

#3x - x^2 - 4 = 8x - 24 - x^2#

We can now add and subtract the necessary terms to isolate the #x# terms while keeping the equation balanced:

#3x - x^2 - 4 - color(red)(3x) + color(blue)(x^2) + color(green)(24) = 8x - 24 - x^2- color(red)(3x) + color(blue)(x^2) + color(green)(24)#

#3x - color(red)(3x) - x^2 + color(blue)(x^2) - 4 + color(green)(24) = 8x - color(red)(3x) - 24 + color(green)(24) - x^2 + color(blue)(x^2)#

#0 - 0 - 4 + color(green)(24) = 8x - color(red)(3x) - 0 - 0#

#- 4 + color(green)(24) = 8x - color(red)(3x)#

#20 = 5x#

Now we can divide each side of the equation by #color(red)(5)# to solve for #x# while keeping the equation balanced:

#20/color(red)(5) = (5x)/color(red)(5)#

#4 = (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5))#

#4 = x#

#x = 4#