Question

I don't understand how to solve the proportion.2x/x+3 = 25/x

Answer 1

Given the following proportion:

$\frac{2x}{x+3}=\frac{25}{x}$

You can solve it by following the steps shown below:

1. You can multiply both sides of the equation by:

$x+3$

Then:

$\begin{gathered} (x+3)(\frac{2x}{x+3})=(\frac{25}{x})(x+3) \\ \\ 2x=\frac{25(x+3)}{x} \\ \\ 2x=\frac{25x+75}{x} \end{gathered}$

2. Now you can multiply both sides of the equation by "x":

$\begin{gathered} (x)(2x)=(\frac{25x+75}{x})(x) \\ \\ 2x^2=25x+75_{} \end{gathered}$

3. Rewrite the Quadratic Equation in the form:

$ax^2+bx+c=0$

Then:

$2x^2-25x-75_{}=0$

4. You can identify that:

$\begin{gathered} a=2 \\ b=-25 \\ c=-75 \end{gathered}$

5. Then, you can use the Quadratic Formula to find the solutions:

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

Substituting values and evaluating, you get:

$\begin{gathered} x=\frac{-(-25)\pm\sqrt[]{(-25)^2-4(2)(-75)}}{(2)(2)} \\ \\ x=\frac{25\pm35}{4} \\ \\ x_1=\frac{25+35}{4}=15 \\ \\ x_2=\frac{25-35}{4}=\frac{-10}{4}=-\frac{5}{2} \end{gathered}$

Therefore, the answer is:

$\begin{gathered} x_1=15 \\ \\ x_2=-\frac{5}{2} \end{gathered}$