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Tpy6a [65]
3 years ago
12

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

Mathematics
1 answer:
diamong [38]3 years ago
3 0
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
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