Question 118090

{{{sqrt(2y+7)+4=y}}} Start with the given equation



{{{sqrt(2y+7)=y-4}}} Subtract 4 from both sides.



{{{2y+7=(y-4)^2}}} Square both sides




{{{2y+7=y^2-8y+16}}}Foil the right side



{{{0=y^2-10y+9}}} Subtract 2y and 7 from both sides




{{{(y-9)(y-1)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{y-9=0}}} or  {{{y-1=0}}} 


{{{y=9}}} or  {{{y=1}}}    Now solve for y in each case



So our possible answers are:

 {{{y=9}}} or  {{{y=1}}}


Check:

Let's check the possible solution {{{y=9}}}

{{{sqrt(2y+7)+4=y}}} Start with the given equation


{{{sqrt(2(9)+7)+4=9}}} Plug in {{{y=9}}}


{{{sqrt(18+7)+4=9}}} Multiply


{{{sqrt(25)+4=9}}} Add


{{{5+4=9}}} Take the square root of 25 to get 5


{{{9=9}}} Add.  Since the two sides of the equation are equal, this verifies our answer.



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Let's check the possible solution {{{y=1}}}

{{{sqrt(2y+7)+4=y}}} Start with the given equation


{{{sqrt(2(1)+7)+4=1}}} Plug in {{{y=1}}}


{{{sqrt(2+7)+4=1}}} Multiply


{{{sqrt(9)+4=1}}} Add


{{{3+4=1}}} Take the square root of 25 to get 5


{{{9=1}}} Add.  Since the two sides of the equation are <b>not</b> equal, this means that {{{y=1}}} is not a valid solution.




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So the only solution is {{{y=9}}}