First, add #color(red)(5)# to each side of the equation to put the equation in standard form:
#x^2 - 4x + 57 + color(red)(5) = -5 + color(red)(5)#
#x^2 - 4x + 62 = 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)(-4)# for #color(blue)(b)#
#color(green)(62)# for #color(green)(c)# gives:
#x = (-color(blue)((-4)) +- sqrt(color(blue)((-4))^2 - (4 * color(red)(1) * color(green)(62))))/(2 * color(red)(1))#
#x = (4 +- sqrt(16 - 248))/2#
#x = (4 +- sqrt(-232))/2#
#x = (4 +- sqrt(4 * -58))/2#
#x = (4 +- sqrt(4)sqrt(-58))/2#
#x = (4 +- 2sqrt(-58))/2#
#x = 2 +- sqrt(-58)#
