What are the steps in factoring the left hand side of this equation as a square?

 

"factor the left hand side as a square for (x^2)+(x/2)+(1/16)=(9/16)"

 

If the left-hand side factors as a square it must have the form (x + k)²

 

Expand this to get  x² + 2kx + k²  which must match x² + x/2 + 1/16

 

Look at the coefficients of x.  To match we must have 2k = 1/2 or k = 1/4.

 

Look at the constant term.  To match we must have k² = 1/16.  Since (1/4)² does indeed equal 1/16 we have consistency.

 

So   (x + 1/4)² = 9/16

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