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

Answer 1

Julia Adams

#x=2/9+-sqrt2/2#

# "add 2 to both sides" #

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

"Take the square root of both sides" #color(blue)

Note that #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" #

#2/3+-(3sqrt2)/2# is #rArr3x.

# "divide both sides by 3" #

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

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Answer 2

Eva Adamson

To solve the equation ((3x-\frac{2}{3})^2 - 2 = \frac{5}{2}), follow these steps:

Add 2 to both sides of the equation.
Simplify the expression inside the parentheses.
Square root both sides of the equation.
Solve for (x).

The solution to the equation is (x = \frac{4}{9}) or (x = \frac{2}{3}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.