# How do you find the x intercepts of  36x^2 + 84x + 49 = 0?

Aug 2, 2017

$y = 36 {x}^{2} + 84 x + 49$ has a single $x$-intercept at $x = - \frac{7}{6}$

#### Explanation:

Technically an equation in one variable does not have intercepts; it has a (or multiple) solution(s).

$36 {x}^{2} + 84 x + 49$
can be factored as ${\left(6 x + 7\right)}^{2} \mathmr{and} \left(6 x + 7\right) \cdot \left(6 x + 7\right)$

So if $36 {x}^{2} + 84 x + 49 = 0$
then $\left(6 x + 7\right) \cdot \left(6 x + 7\right) = 0$
which implies $\left(6 x + 7\right) = 0$
$\textcolor{w h i t e}{\text{xxxxxxxx}} x = - \frac{7}{6}$

Aug 2, 2017

See a solution process below:

#### Explanation:

We can factor the left side of the equation as:

${\left(6 x + 7\right)}^{2} = 0$

Or

$\left(6 x + 7\right) \left(6 x + 7\right) = 0$

Because both terms on the left are the same there will be only one $x$ intercept. We can solve one of the terms for $0$:

$6 x + 7 = 0$

$6 x + 7 - \textcolor{red}{7} = 0 - \textcolor{red}{7}$

$6 x + 0 = - 7$

$6 x = - 7$

$\frac{6 x}{\textcolor{red}{6}} = - \frac{7}{\textcolor{red}{6}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} x}{\cancel{\textcolor{red}{6}}} = - \frac{7}{\textcolor{red}{6}}$

$x = - \frac{7}{6}$

As you can see from the graph the parabola touches the x-axis at just one point: $- \frac{7}{6}$ or $\left(- \frac{7}{6} , 0\right)$

graph{(y - 36x^2 - 84x - 49)((x+7/6)^2+(y)^2-0.0005) = 0 [-2, 0, -0.5, 0.51]}