Question 243560

{{{(5x+3)^2-5=49}}} Start with the given equation.



{{{(5x+3)^2=49+5}}}Add {{{5}}} to both sides.



{{{(5x+3)^2=54}}} Combine like terms.



{{{5x+3=""+-sqrt(54)}}} Take the square root of both sides.



{{{5x+3=sqrt(54)}}} or {{{5x+3=-sqrt(54)}}} Break up the "plus/minus" to form two equations.



{{{5x+3=3*sqrt(6)}}} or {{{5x+3=-3*sqrt(6)}}}  Simplify the square root.



{{{5x=-3+3*sqrt(6)}}} or {{{5x=-3-3*sqrt(6)}}} Subtract {{{3}}} from both sides.



{{{x=(-3+3*sqrt(6))/5}}} or {{{x=(-3-3*sqrt(6))/5}}} Divide both sides by 5.



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Answer:



So the solutions are {{{x=(-3+3*sqrt(6))/5}}} or {{{x=(-3-3*sqrt(6))/5}}}.