First, put the equation in standard form:
#8m^2 - 2m - color(red)(7) = 7 - color(red)(7)#
#8m^2 - 2m - 7 = 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)(8)# for #color(red)(a)#
#color(blue)(-2)# for #color(blue)(b)#
#color(green)(-7)# for #color(green)(c)# gives:
#x = (-color(blue)(-2) +- sqrt(color(blue)(-2)^2 - (4 * color(red)(8) * color(green)(-7))))/(2 * color(red)(8))#
#m = (2 +- sqrt(4 - (32 * color(green)(-7))))/16#
#m = (2 +- sqrt(4 - (-224)))/16#
#m = (2 +- sqrt(4 + 224))/16#
#m = (2 +- sqrt(228))/16#
#m = (2 +- sqrt(4 * 57))/16#
#m = (2 +- sqrt(4)sqrt(57))/16#
#m = (2 +- 2sqrt(57))/16#
#m = 2/16 +- (2sqrt(57))/16#
#m = 1/8 +- sqrt(57)/8#
#m = (1 +- sqrt(57))/8#
The Solution Set Is:
#m = { ((1 - sqrt(57))/8), ((1 + sqrt(57))/8)}#
