How do you solve using the completing the square method #3x^2 + 15x = 9#?

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Answer 1 · 2016-03-09T06:50:17

#x=(-5+sqrt37)/2# and #x=(-5-sqrt37)/2#

From the given

#3x^2+15x=9#

divide both sides of the equation by 3 first, to make the coefficient of #x^2# equal to 1

#(3x^2)/3+(15x)/3=9/3#

#x^2+5x=3#

Divide now the numerical coefficient of x by 2 then square the result. Let the result be added to both sides of the equation

#x^2+5x+25/4=3+25/4#

We now have the Perfect Square Trinomial
#(x+5/2)^2=37/4#
Extract square root of both sides

#sqrt((x+5/2)^2)=sqrt(37/4)#

#x+5/2=+-1/2sqrt(37)#

#x=-5/2+-1/2sqrt(37)#

we have 2 values

#x=-5/2+1/2sqrt(37)# and #x=-5/2-1/2sqrt(37)#

God bless....I hope the explanation is useful.