Question

Solve 3x2 = −12x − 15. x = −4 ± 2i x = −4 ± i x = −2 ± 2i x = −2 ± i

Answer 1

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;

$x + 2 = \pm \sqrt{ - 1}$

We add -2 to both sides,

$x = - 2 \pm \sqrt{ - 1}$

We simplify to obtain,

$x = - 2 \pm i$