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)}
