First, put the equation in standard quadratic form:
#color(red)(u^2) + 6u + 2 = color(red)(u^2) - u^2#
#u^2 + 6u + 2 = 0#
or
#1u^2 + 6u + 2 = 0#
Now, use the quadratic formula to solve for #u#. 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)(6)# for #color(blue)(b)#
#color(green)(2)# for #color(green)(c)# gives:
#u = (-color(blue)(6) +- sqrt(color(blue)(6)^2 - (4 * color(red)(1) * color(green)(2))))/(2 * color(red)(1))#
#u = (-color(blue)(6) +- sqrt(36 - 8))/2#
#u = (-color(blue)(6) +- sqrt(28))/2#
#u = (-color(blue)(6) +- sqrt(4 * 7))/2#
#u = (-color(blue)(6) +- sqrt(4)sqrt(7))/2#
#u = (-color(blue)(6) +- 2sqrt(7))/2#
#u = -6/2 +- (2sqrt(7))/2#
#u = -3 +- sqrt(7)#
The Solution Set Is:
#u = {-3 - sqrt(7), -3 + sqrt(7)}#
