How do you solve #x^2-4x-11=0# using the quadratic formula?

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Answer 1 · 2018-01-25T12:51:11

See a solution process below:

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)(-11)# for #color(green)(c)# gives:

#x = (-color(blue)(-4) +- sqrt(color(blue)(-4)^2 - (4 * color(red)(1) * color(green)(-11))))/(2 * color(red)(1))#

#x = (color(blue)(4) +- sqrt(16 - (-44)))/2#

#x = color(blue)(4)/2 +- sqrt(16 + 44)/2#

#x = 2 +- sqrt(60)/2#

#x = 2 +- sqrt(4 * 15)/2#

#x = 2 +- (sqrt(4)sqrt(15))/2#

#x = 2 +- (2sqrt(15))/2#

#x = 2 +- sqrt(15)#