Solve 3x squared minus x minus 1 =0

Question

Hi I’m doing maths homework and was wondering how to work this question out in steps so I understand.

Answer 1

3x²-x-1=0 (we can solve this using the quadratic formula)

SOLUTION BY COMPLETNG THE SQUARE

Divide through by 3:

x²-x/3-1/3=0

Take half the coefficient of the x term and square it: so we halve 1/3 to get 1/6, and square it to get 1/36.

Move the constant to the other side of the equals sign:

x²-x/3=1/3

Now add 1/36 to both sides:

x²-x/3+1/36=1/3+1/36=12/36+1/36=13/36.

We just completed the square on the left hand side:

(x-1/6)²=13/36

Now we take the square root of each side:

x-1/6=±√(13/36)=±√13/6

So x=1/6±√13/6 or (1±√13)/6. This gives us 2 values for x=(1+√13)/6=0.7676 and (1-√13)/6=-0.4343 approx.

Using the quadratic formula gives us the same result.