Confused

Note that   (10x - 3)²   =   (10x - 3)(10x - 3)   =   100x² - 60x + 9

Now let's look at the given equation:

5x² + 4  =  3x + 9

                                Subtract  3x  from both sides of the equation.

5x² - 3x + 4  =  9

                                Subtract  4  from both sides of the equation.

5x² - 3x  =  5

                                Multiply through by  20

100x² - 60x  =  100

                                         Add  9  to both sides of the equation.

100x² - 60x + 9   =   109

                                         And remember that  100x² - 60x + 9  =  (10x - 3)²

(10x - 3)²   =   109

5x^2 + 4  = 3x + 9                  

5x^2 - 3x - 5  = 0       use the Quadratic Formula                  

3 ±√[ 109]

___________   =   x       which implies that

        10

10x  =  3 ±√109          subtract 3 from both sides

10x - 3  =  ±√109       square both sides

So

(10x - 3)^2  = ( ±√109)^2  =

109