How do you solve #3x^2 + 10x = 8# by completing the square?

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Answer 1 · 2016-05-12T21:22:48

#x=2/3# or #x=-4#

Multiply by #3# and add #25# to both sides to get:

#9x^2+30x+25=24+25#

which simplifies to:

#(3x+5)^2 = 49 = 7^2#

So #(3x+5)# is a square root of #7^2#, so it must be #7# or #-7#:

#3x+5 = +-7#

If #3x+5 = 7#, then #3x=2#, so #x=2/3#

If #3x+5 = -7#, then #3x=-12#, so #x=-4#