Question

Find the real solutions of the quadratic equation $\frac{x^2}{x+100}=50$.

Short answer

The two distinct real solutions of given quadratic equation are $x=100,-50$.

Step-by-step solution

Step 1. By method of quadratic formula.

The roots of the quadratic equation of the form $a{x}^2+bx+c=0$where $a\ne 0$can be evaluated by using the quadratic formula shown below.

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

Step 2. Find roots of quadratic equation by quadratic formula.

The given quadratic equation is $\frac{x^2}{x+100}=50$which can be written as $x^2-50x-5000=0$whose roots can be evaluated by quadratic formula as shown below.

localid="1645704510375" $$\begin{gathered} x=\frac{-\left(-50\right)\pm \sqrt{{\left(-50\right)}^2-4\left(1\right)\left(-5000\right)}}{2\left(1\right)} \\ =\frac{50\pm \sqrt{22500}}{2} \\ =\frac{50\pm 150}{2} \\ =100,-50 \end{gathered}$$

Step 3. Description of steps.

The given quadratic equation has two distinct real solutions $x=100,-50$.