How do you solve #–4 sqrt(x+2) + 3 = -9#?

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Answer 1 · 2016-06-20T03:33:20

#x=7#

First, isolate the term including #x# using subtraction.

#-4sqrt(x+2)+3 = -9#

#=>-4sqrt(x+2)+3-3 = -9 - 3#

#=> -4sqrt(x+2) = -12#

Next, change the coefficient of #sqrt(x+2)# to #1# using division.

#=> (-4sqrt(x+2))/(-4) = (-12)/(-4)#

#=> sqrt(x+2) = 3#

Next, eliminate the square root by squaring each side.

#=>(sqrt(x+2))^2 = 3^2#

#=> x+2 = 9#

Finally, isolate #x# using subtraction.

#=> x+2-2 = 9-2#

#=>x = 7#

And, as good practice, check your answer:

#-4sqrt(7+2)+3 = -4sqrt(9)+3#

#=-4(3)+3#

#=-12+3#

#=-9#

as desired.