# Question #d2d79

Jul 29, 2017

$x = 65 + \sqrt{2125} = 111.1$

$x = 65 - \sqrt{2125} = 18.9$

#### Explanation:

You have got to the step of $1425 = \left(125 - x\right) \left(x - 5\right)$

Now get rid of the brackets, and you will end up with an ${x}^{2}$ term.
That means it is a quadratic equation.

Make it equal to $0$ and then decide on an appropriate method of solving..

$\textcolor{w h i t e}{\times \times \times \times \times \times x} 1425 = \left(125 - x\right) \left(x - 5\right)$

$\textcolor{w h i t e}{\times \times \times \times \times \times x} 1425 = 125 x - 625 - {x}^{2} + 5 x$

${x}^{2} - 130 x + 625 + 1475 = 0$

$\textcolor{w h i t e}{\times \times x} {x}^{2} - 130 x + 2100 = 0$

Complete the square:

${x}^{2} - 130 x \textcolor{w h i t e}{\times \times} = - 2100 \text{ } \leftarrow {\left(\frac{- 160}{2}\right)}^{2} = {65}^{2}$

${x}^{2} - 130 x + {65}^{2} = - 2100 + {65}^{2}$

${\left(x - 65\right)}^{2} = 2 , 125$

$x - 65 = \pm \sqrt{2125}$

$x = 65 + \sqrt{2125} = 111.1$

$x = 65 - \sqrt{2125} = 18.9$