# How do you solve the proportion (x-1)/4 = 5/(x+7)?

May 16, 2016

$x = - 3 \pm 2 i$

#### Explanation:

Cross multiply$\text{ "->" } \left(x - 1\right) \left(x + 7\right) = 20$

${x}^{2} + 6 x - 7 = 20$

${x}^{2} + 6 x + 13 = 0$

Complete the square

${\left(x + 3\right)}^{2} + 13 + k = 0$

$k = \left(- 1\right) \times {3}^{2} = - 9$

${\left(x + 3\right)}^{2} + 4 = 0$

$x + 3 = \pm \sqrt{- 4}$

There is no solution for the set of numbers 'Real' $\to x \notin \mathbb{R}$
There is a solution for the set of numbers 'Complex' $\to x \in \mathbb{C}$

$x + 3 = \pm 2 i$

$x = - 3 \pm 2 i$