Question

Use the method of completing the square to solve the quadratic equation, expressing your solution in the form a±b√n, where a, b and n are rational.
3x^2 - 6x+1=0

Answer 1

The objective of completing the square is to make a perfect square.
(a+b)^2= a^2 + 2ab+ b^2

Answer 2

Make the coefficient of the x^2=1 and move the constant to the right.
What is 1/2 the coefficient of the term with x? This will be your b
What is the value of b^2?
To put in the format desired you had to add b^2 on the right. This is an equation so do the same to the other side to maintain the balance
Now take the square root of each side.
You need to solve for x so subtract b from each side.

Answer 3

Let me know if you have any questions about these steps.

Answer 4

If 3x^2-6x+1=0 and we want to complete the square, a smart first move would be to divide the entire equation by 3 (the coefficient of the x^2 term). We'd get this factored form:

3(x^2-2x + 1/3) = 0.

Answer 5

Now, focus on completing the square in the case of:\[x^2-2x +1=0.\]

Answer 6

Next, focus on completing the square in the quantity inside parentheses:\[x^2-2x+\frac{ 1 }{ 3 }=0\]

Answer 7

As Tricia suggested, take half of the coefficient of x, which is 1/2 of -2, or just -1.
Square this. Add, and then subtract, that result:\[x^2-2x +1-1+\frac{ 1 }{ 3 }=0\]

Answer 8

Do you see a perfect square in the above equation? If so, write it in the form (x-a)^2.

Answer 9

Your turn.