# How do you solve 9x² + 42x = -49?

Jun 6, 2018

$x = - \frac{7}{3}$

#### Explanation:

$9 {x}^{2} + 42 x = - 49$

Move all terms to LHS

$9 {x}^{2} + 42 x + 49 = 0$

Now we factor

$\left(3 x + 7\right) \left(3 x + 7\right) = 0$

${\left(3 x + 7\right)}^{2} = 0$

Now we solve for $x$

$3 x + 7 = 0$

$3 x = - 7$

$x = - \frac{7}{3}$

Although this is a polynomial of degree $2$ and you would expect $2$ solutions, it turns out that there is one redundant solution, namely $x = - \frac{7}{3}$.