Another one involving completing the square

x2 + 3x + 5/4 = 0          re-arrange to:   x^2 +3x = - 5/4

Now take 1/2 of the x coefficient (3) then square it and add it to both sides

x^2 + 3x + 9/4 = -5/4 + 9/4

(x+ 3/2)^2  =  4/4 =1

Take sqrt of both sides

x+3/2  =  +1 or -1

so   x = -1/2  or -5/2

(X+3)^2 +(X^2 -13/2)=0

 

X^2 +6X +9  +X^2 -13/2  =0

2X^2  +6X +18/2  -13/2 =0

2X^2  +6X  +5/2           =0   now divide through by 2 to get

X^2 +3X +5/4              =0      now complete the square

(X +3/2)^2 - 1              =O

(X+3/2)^2                    =1

(X+3/2)                       =  1        and    -1   so X= -1/2     and  X= -5/2