How do you factor #4x^2+12x=9#?

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Answer 1 · 2018-08-10T17:34:29

# x=3/2(-1+-sqrt2)#.

Observe that, the last term obtained on completing the square of

#4x^2+12x# is #9#.

So, adding #9# on both sides of the given eqn., we get,

#4x^2+12x+9=9+9, #

# i.e., (2x+3)^2=18=(3sqrt2)^2#.

Taking square root, #2x+3=+-3sqrt2#.

#:. 2x=-3+-3sqrt2=3(-1+-sqrt2)#.

#:. x=3/2(-1+-sqrt2)#.