<PRE><B>Question 130869</B>

*[Tex \LARGE (2x-3)^2=25] Start with the given equation




*[Tex \LARGE 2x-3=\pm sqrt{25}] Take the square root of both sides





*[Tex \LARGE 2x-3=\pm 5] Take the square root of 25 to get 5




*[Tex \LARGE 2x=3\pm 5] Add 3 to both sides.



 Break down the expression into two parts:




 &lt;pre&gt;

 *[Tex \LARGE 2x=3+5]  &lt;font size=&quot;6&quot;&gt;or&lt;/font&gt;  *[Tex \LARGE 2x=3-5]

 &lt;/pre&gt;


 Now combine like terms for each expression:

 &lt;pre&gt;

 *[Tex \LARGE 2x=8]  &lt;font size=&quot;6&quot;&gt;or&lt;/font&gt;   *[Tex \LARGE 2x=-2]   &lt;/pre&gt;


Divide both sides by 2 to isolate x

 &lt;pre&gt;

 *[Tex \LARGE x=4]  &lt;font size=&quot;6&quot;&gt;or&lt;/font&gt;   *[Tex \LARGE x=-1]   &lt;/pre&gt;



-----------------------------------

Answer:

So our solution is

 &lt;pre&gt;

*[Tex \LARGE x=4]  &lt;font size=&quot;6&quot;&gt;or&lt;/font&gt;   *[Tex \LARGE x=-1]
 &lt;/pre&gt;


 Notice when we graph the equations {{{y=(2x-3)^2}}} and {{{y=25}}}  we get:


{{{drawing(500, 500, -7, 13, -10, 30,
graph( 500, 500, -7, 13, -10, 30, (2x-3)^2,25)
)}}} graph of  {{{y=(2x-3)^2}}} (red) and {{{y=25}}} (green)




Here we can see that the two equations intersect at x values of {{{x=-2}}} and {{{x=4}}}, so this verifies our answer.

 </PRE>