How do you solve rational equations #81.9=((0.1+2x)^2)/((0.1-x)(0.1-x))#?

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Answer 1 · 2018-02-08T20:11:15

#x=0.0488# or #x=0.213# (3sf)

#81.9=((0.1+2x)^2)/((0.1-x)(0.1-x)#

We can rewrite the dominator, to get

#81.9=((0.1+2x)^2)/((0.1-x)^2#

Multiply by #(0.1-x)^2#

#81.9(0.1-x)^2=(0.1+2x)^2#

Expand the brackets

#81.9(0.01-0.2x+x^2)=(0.01+0.4x+4x^2)#

#0.819-16.38x+81.9x^2=0.01+0.4x+4x^2#

#77.9x^2-20.38x+0.809=0#

#x=(20.38+-sqrt(20.38^2-4xx77.9xx0.809))/(2xx77.9)#

#x=0.0488# or #x=0.213# (3sf)