Question

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

Answer 1

Answer:

The solutions are

$x=1+\sqrt{\frac{7}{3}}$

$x=1-\sqrt{\frac{7}{3}}$

Step-by-step 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

$3(x-1)^{2}=7$

$(x-1)^{2}=\frac{7}{3}$

square root both sides

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

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

$x=1+\sqrt{\frac{7}{3}}$

$x=1-\sqrt{\frac{7}{3}}$