How do you solve the equation (3x-2/3)^2-2=5/2?

1 Answer
Jim G.
Feb 21, 2018

x=2/9+-sqrt2/2

Explanation:

"add 2 to both sides"

rArr(3x-2/3)^2=9/2

color(blue)"take square root of both sides"

sqrt((3x-2/3)^2)=+-sqrt(9/2)larrcolor(blue)"note plus or minus"

rArr3x-2/3=+-3/sqrt2=+-3/sqrt2xxsqrt2/sqrt2=(3sqrt2)/2

"add "2/3" to both sides"

rArr3x=2/3+-(3sqrt2)/2

"divide both sides by 3"

rArrx=2/9+-sqrt2/2larrcolor(red)"exact values"

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