# How do you solve 64x^2 - 144x + 81 = 0?

May 18, 2015

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

where $a = 64$, $b = - 144$ and $c = 81$.

$\frac{144 \pm \sqrt{{144}^{2} - 4 \left(64\right) \left(81\right)}}{128}$

$\frac{144 \pm \sqrt{20736 - 20736}}{128}$

$\frac{144 \pm \sqrt{0}}{128}$

$\frac{144}{128} = \textcolor{g r e e n}{\frac{9}{8}}$

Your quadratic function is tangent to axis $x$, touching it only in the point with $x$ coordinate $\left(\frac{9}{8}\right)$. So, we can say that ${x}_{1} = {x}_{2} = \frac{9}{8}$

May 18, 2015

$y = {\left(8 x - 9\right)}^{2} = 64 {x}^{2} - 144 x + 81.$ = 0, then:

$\left(8 x - 9\right) = 0 \to x = \frac{9}{8.}$ There is double root.