Question

Find the real solutions of the quadratic equation $x^2+5x-6=0$.

Short answer

The real solution of the quadratic equation are $x=-6\text{and}x=1$.

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 $x^2+5x-6=0$whose roots can be evaluated by quadratic formula as shown below.

$$\begin{gathered} x=\frac{-\left(5\right)\pm \sqrt{{\left(5\right)}^2-4\left(1\right)\left(-6\right)}}{2\left(1\right)} \\ =\frac{-5\pm \sqrt{49}}{2} \\ =\frac{-5\pm 7}{2} \\ =1,-6 \end{gathered}$$

Step 3. DESCRIPTION OF STEPS.

The real solutions of the equation are $x=-6\text{and}x=1$.