SOLUTION: I am stumped...I can not figure these two problems out for the life of me...can someone please assist me with these two problems? Find all real solutions to each equation. 64

 

We group the first two terms as one term:



Now there are three terms on the left.  Notice 
that if we square the variable of the
middle term , we get the 
variable of the first term .

Therefore we substitute the letter "" for
the variable of the middle term, that is



Then squaring both sides we have



So we substitute and



becomes simply



Which we factor 



and solve getting  and 

Since  and a square root
can never be negative in real numbers, we can 
rule out . So 

Substituting back



becomes





We use the quadratic formula:

  

 

 

 

--------------------------------

Find all real and imaginary solutions to each equation. 
70) 

Notice that if we square the variable of the
middle term , we get the 
variable of the first term .

Therefore we substitute the letter "" for
the variable of the middle term, that is



and squaring both sides:



So we substitute and



becomes simply



Which we factor 



and solve getting  and 

Now since , we have

 and 

Taking square roots:

 and 

or

=± and =±

Edwin