Question 76932
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Square root of 2X + 3 = 2X - 3 

{{{sqrt(2X+3)=2X-3}}}

Square both sides:

{{{(sqrt(2X+3))^2=(2X-3)^2}}}

{{{2X+3=(2X-3)(2X-3)}}}

Use FOIL on the right

{{{2X+3=4X^2-6X-6X+9}}}

{{{2X+3=4X^2-12X+9}}}

Get 0 on the left by adding
-2X-3 to both sides

{{{0=4X^2-14X+6}}}

Divide every term by 2

{{{0/2=(4X^2)/2-(14X)/2+6/2}}}

{{{0=2X^2-7X+3}}} 

Factor the right hand side:

{{{0=(X-3)(2X-1)}}}

Set each factor = 0

{{{0=X-3}}}

{{{3=X}}}

That's one answer.

{{{0=2X-1}}}

{{{1=2X}}}

{{{1/2=X}}}

That's the other answer.

You MUST ALWAYS check
even-root equations for
extraneous answers:

Checking the answer x=3

{{{sqrt(2X+3)=2X-3}}}

{{{sqrt(2(3)+3)=2(3)-3}}}

{{{sqrt(6+3)=6-3}}}
{{{sqrt(9)= 3}}}
{{{3=3}}}

That checks, so the answer x=3 is a solution.

Checking the answer x=1/2

{{{sqrt(2X+3)=2X-3}}}

{{{sqrt(2(1/2)+3)=2(1/2)-3}}}

{{{sqrt(1+3)=1-3}}}
{{{sqrt(4)= -2}}}
{{{2=-2}}}

That DOES NOT check, so the answer x=1/2
is NOT a solution.

The only solution is X=3

Edwin</pre>