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}#
