Question

Find the real solutions of the quadratic equation $25x^2+7x+49=0$.

Short answer

The given equation has exactly one real solution $x=-\frac{7}{5}$.

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$25x^2+7x+49=0$ whose roots can be evaluated by quadratic formula as shown below.

$$\begin{gathered} x=\frac{-\left(70\right)\pm \sqrt{{\left(70\right)}^2-4\left(25\right)\left(49\right)}}{2\left(25\right)} \\ =\frac{-70\pm \sqrt{0}}{50} \\ =\frac{-70}{50} \\ =-\frac{7}{5} \end{gathered}$$

Step 3. DESCRIPTION OF STEPS.

The given quadratic equation has only one real solution $x=-\frac{7}{5}$.