How do you solve 6x^2+72=0?

Oct 27, 2016

There are no value Real solutions to this equation.
Using Complex values $x = \pm 2 \sqrt{3} i$

Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} 6 {x}^{2} + 72 = 0$

Dividing both sides by $6$ gives
$\textcolor{w h i t e}{\text{XXX}} {x}^{2} + 12 = 0$

$\textcolor{w h i t e}{\text{XXX}} {x}^{2} = - 12$

...for all Real values of $x$ we know that ${x}^{2} \ge 0$
so there can be no Real valued solutions.

$\textcolor{w h i t e}{\text{XXX}} {x}^{2} = {\left(2 \sqrt{3}\right)}^{2} \times \left(- 1\right)$

$\textcolor{w h i t e}{\text{XXX}} x = \pm 2 \sqrt{3} \times \sqrt{- 1}$

$\textcolor{w h i t e}{\text{XXX}} x = \pm 2 \sqrt{3} i$