How do you solve #8x=x^2-9# using the quadratic formula?

1 Answer
Mar 10, 2018

Answer:

See a solution process below:

Explanation:

First, subtract #color(red)(8x)# from each side of the equation to put the equation in standard quadratic form:

#8x - color(red)(8x) = x^2 - color(red)(8x) - 9#

#0 = x^2 - 8x - 9#

#x^2 - 8x - 9 = 0#

We can now use the quadratic equation to solve this problem:

The quadratic formula states:

For #color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0#, the values of #x# which are the solutions to the equation are given by:

#x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))#

Substituting:

#color(red)(1)# for #color(red)(a)#

#color(blue)(-8)# for #color(blue)(b)#

#color(green)(-9)# for #color(green)(c)# gives:

#x = (-color(blue)(-8) +- sqrt(color(blue)(-8)^2 - (4 * color(red)(1) * color(green)(-9))))/(2 * color(red)(1))#

#x = (8 +- sqrt(64 - (-36)))/2#

#x = (8 +- sqrt(64 + 36))/2#

#x = (8 - sqrt(100))/2#; #x = (8 + sqrt(100))/2#

#x = (8 - 10)/2#; #x = (8 + 10)/2#

#x =(-2)/2#; #x = 18/2#

#x =-1#; #x = 9#

The Solution Set Is:

#x ={-1, 9}#