Question

How would you solve 2x^2 -4x -3 = 0

Answer 1

ANSWER

$x =1 +\frac{1}{2} \sqrt{ 10} \: or \: x =1 - \frac{1}{2}\: \sqrt{10}$

EXPLANATION

The given quadratic equation is

$2 {x}^{2} - 4x - 3 = 0$

This function is of the form:

$a{x}^{2} + bx + c = 0$

This implies that:

a=2, b=-4 and c=-3.

We can solve this equation using the quadratic formula:

$x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a}$

We substitute the values into the quadratic formula to obtain;

$x = \frac{ - - 4 \pm \: \sqrt{ {( - 4)}^{2} - 4(2)( - 3)} }{2(2)}$

$x = \frac{4 \pm \: \sqrt{ 40} }{4}$

$x = \frac{4 \pm \: 2\sqrt{ 10} }{4}$

$x =1\pm \: \frac{1}{2} \sqrt{10}$

$x =1 +\frac{1}{2} \sqrt{ 10} \: or \: x =1 - \: \frac{1}{2} \sqrt{10}$