Question 103650
*[Tex \LARGE 5(x-2)^2=3] Start with the given equation





{{{(x-2)^2=3/5}}} Divide both sides by 5



*[Tex \LARGE x-2=\pm sqrt{\frac{3}{5}}] Take the square root of both sides




*[Tex \LARGE x=2\pm sqrt{\frac{3}{5}}] Add 2 to both sides to isolate x.





*[Tex \LARGE x=2\pm \frac{sqrt{3}}{sqrt{5}}] Break up the root



*[Tex \LARGE x=2\pm \left(\frac{sqrt{3}}{sqrt{5}}\right)\left(\frac{sqrt{5}}{sqrt{5}}\right)] Multiply by {{{sqrt(5)/sqrt(5)}}} to rationalize the denominator



*[Tex \LARGE x=2\pm \frac{sqrt{15}}{sqrt{25}}] Multiply




*[Tex \LARGE x=2\pm \frac{sqrt{15}}{5}] Simplify



*[Tex \LARGE x=\frac{10}{5}\pm \frac{sqrt{15}}{5}] Rewrite {{{2}}} as {{{10/5}}}



*[Tex \LARGE x=\frac{10\pm sqrt{15}}{5}] Combine the fractions


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Answer:


So our solution is:


*[Tex \LARGE x=\frac{10\pm sqrt{15}}{5}]



So the answer is C