# How do you solve the quadratic 9a^2+3=-27 using any method?

Sep 7, 2016

There is no solution

#### Explanation:

first subtract by $3$

$9 {a}^{2} = - 30$

divide by $9$
${a}^{2} = - \frac{30}{9}$

now take the square root but wait we can't do that for a negative so there is no solution.

You can try the quadratic formula but lets see what happens when we try that approach

$\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$\frac{0 \pm \sqrt{0 - 4 \cdot 30}}{2} = \frac{\sqrt{- 120}}{2}$

Okay wait we see the same thing here, we cant really take the square root of a negative.

Lastly anytime you have an even exponent the answer will always be positive so this is rational enough to consider this an equation with no solution.