How to solve? without quadratic formula?

Question

1/3x^2+3x-4=0

simplifiying the x2 gets me confused

Answer 1

(1/3)x² + 3X - 4 = 0

 

FIRST, JUST MULT BOTH SIDES BY 3. 

 

X² + 9X - 12 = 0

 

METHOD OF COMPLETING THE SQUARE

MOVE THE CONST TO THE OTHER SIDE (ADD 12 TO BOTH SIDES)

 

X² + 9X  = 12

 

NOW, ADD (B/2)²  TO EACH SIDE  (B IN THIS CASE = 9)

X² + 9X + (9/2)²  =  12 + (9/2)²

 

NOW WE HAVE A PERFECT SQUARE ON LEFT SIDE 

 

(X + 9/2)²   =  12 + 81/4  =  (48 + 81)/4 = 129/4

(X + 9/2)²  =  129/4

 

NOW, TAKE SQUARE ROOT OF EACH SIDE: (ALWAYS NEED THE +/- )

 

X + 9/2  = +/- SQRT(129/4) = +/- SQRT(129)/2

 

OR

 

X =  -9/2  +/- SQRT(129) / 2

 

 

WHICH IS TO 3 PLACES, X = -10.179, +1.179