How do you find the missing number or term to make a perfect square trinomial. #x^2 + 10x + c #?

1 Answer
Jun 7, 2015

A perfect square trinomial would be #color(blue)(a^2)+color(purple)(2ab)+color(red)(b^2)#

Here : #color(blue)(a=x)#
#color(purple)(2ab=10x)#
And #color(red)(b^2=c)#

Thus :

#color(blue)acolor(red)b=5x# ( we divide by #2# on bothside )
#color(blue)x*color(red)b=5x# ( since #color(blue)(a=x)# )
#cancelx*color(red)b=cancelx*5#
#color(red)(b=5)#

And thus :

#color(red)(c=b^2=5^2=25#