completing the square

Question

Solve by completing the square... 

3x^2-12x+1=0

Answer 1

3x²-12x+1=0   Subtract 1 from both sides.

3x²-12x=-1     Divide everything by the coefficient on the x² term. (In this case 3)

x²-4x=-1/3                  Take x coefficient (-4) and divide it in half --> -2.  Take this number, square it and add it to both sides. (-2)² = 4

x²-4x+4=-1/3+4          Factor the left side of the equation.

(x-2)² = 11/3            Take the square root of both sides. (Don't forget +/-)

x-2 = ±√(11⁄3)         Add 2 to both sides.

x=2±√(11⁄3)  or written separately...

x=2+√(11⁄3) and x=2-√(11⁄3)

 

 

 

Answer 2

Nataly:

Use the following steps to complete the square and solve for x:

Start with original Equation:  3x²-12x+1=0

Subtract constant term from both sides:  3x²-12x=-1

Divide both sides by coefficient of x² (i.e., divide by 3):  x²-4x=-1/3

Take 1/2 of coefficient of x (-4/2), square it (4),  & add to both sides:  x²-4x+4=-1/3+4

Factor the left side of the equation & simplify right side:  (x-2)²=-1/3+12/3

                                                                               (x-2)²=11/3

Take the square root of both sides:  (x-2)=+/- SQRT(11/3)

Add 2 to both sides to solve for x:  x= 2 +/- SQRT (11/3)