# When Chloe's height is squared and then doubled the result in 3m more than her height now. How tall is Chloe now?

Jan 29, 2016

Chloe is $1.5 \text{m}$ tall.

#### Explanation:

Let $h$ represent Chloe's height in meters. Then:

$2 {h}^{2} = h + 3$

$\implies 2 {h}^{2} - h - 3 = 0$

Applying the quadratic formula , we get

$h = \frac{- \left(- 1\right) \pm \sqrt{{\left(- 1\right)}^{2} - 4 \left(2\right) \left(- 3\right)}}{2 \left(2\right)}$

$= \frac{1 \pm \sqrt{25}}{4}$

$= - 1$ or $\frac{6}{4}$

We know Chloe's height must be positive, and so we can toss out the $- 1$ result, leaving us with

$h = \frac{6}{4}$

Thus Chloe is $1.5 \text{m}$ tall.