Question

Solve 3x2 = −12x − 15.

x = −4 ± 2i
x = −4 ± i
x = −2 ± 2i
x = −2 ± i

Answer 1

d

Explanation:

Answer 2

ANSWER


`x = - 2 \pm i`

EXPLANATION

We use the method of completing the squares.

The equation is

`3 {x}^(2) = - 12x - 15`

We rewrite the above equation to obtain;


`3 {x}^(2) + 12x = - 15`

We divide through by 3 to obtain;


`{x}^(2) + 4x = - 5`

We add half the coefficient of

`x`

to both sides of the equation to get,


`{x}^(2) + 4x + {2}^(2) = - 5 + {2}^(2)`

The right hand side is now a perfect square.


`{(x + 2)}^(2) = - 1`

We now take square root of both sides to get;


`x + 2 = \pm √( - 1)`

We add -2 to both sides,


`x = - 2 \pm √( - 1)`

We simplify to obtain,


`x = - 2 \pm i`