Question

Solve the quadratic equation by completing the square. 3x2 - 6x - 4 = 0

Answer 1

Answer: is in picture below

Explanation:

Answer 2

The solutions are

`x=1+\sqrt{(7)/(3)}`

`x=1-\sqrt{(7)/(3)}`

Explanation:

we have

`3x^(2)-6x-4=0`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`3x^(2)-6x=4`

Factor the leading coefficient

`3(x^(2)-2x)=4`

Complete the square. Remember to balance the equation by adding the same constants to each side

`3(x^(2)-2x+1)=4+3`

`3(x^(2)-2x+1)=7`

Rewrite as perfect squares

`3(x-1)^(2)=7`

`(x-1)^(2)=(7)/(3)`

square root both sides

`x-1=(+/-)\sqrt{(7)/(3)}`

`x=1(+/-)\sqrt{(7)/(3)}`

`x=1+\sqrt{(7)/(3)}`

`x=1-\sqrt{(7)/(3)}`