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

1 Answer
Feb 8, 2018

x=0.0488 or x=0.213 (3sf)

Explanation:

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

From the quadratic formula:

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

x=0.0488 or x=0.213 (3sf)