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

Question

asked Jul 5, 2020 72.3k views

2 Answers

Ramin Afshar · Answer 1 · 2020-07-12T14:44:58+0000

Answer:

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

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

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

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

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