How do you use the quadratic formula to solve #a^2 - 28a +192=0#?

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Answer 1 · 2017-08-07T02:44:28

See a solution process below:

We can use the quadratic equation to solve this problem:

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)(-28)# for #color(blue)(b)#

#color(green)(192)# for #color(green)(c)# gives:

#a = (-color(blue)(-28) +- sqrt(color(blue)((-28))^2 - (4 * color(red)(1) * color(green)(192))))/(2 * color(red)(1))#

#a = (color(blue)(28) +- sqrt(color(blue)(784) - 768))/2#

#a = (color(blue)(28) +- sqrt(16))/2#

#a = (color(blue)(28) + 4)/2# and #a = (color(blue)(28) - 4)/2#

#a = 32/2# and #a = 24/2#

#a = 16# and #a = 12#