Question

In the following exercises, solve by using the Quadratic Formula.
$(x+1)(x-3)=2$

Short answer

The solutions of the given equation are $x=1\pm \sqrt{6}$.

Step-by-step solution

Step 1. Write the quadratic equation in standard form.

The given equation is:

$(x+1)(x-3)=2$

The given equation can be written as:

$\begin{array}{rcl}{x}^2-3x+x-3& =& 2\\ x^2-2x-3-2& =& 0\\ x^2-2x-5& =& 0\end{array}$

Step 2. Substitute the values in Quadratic Formula.

Quadratic Formula for the equation $a{x}^2+bx+c=0$is:

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

In the given equation, $a=1,b=-2,c=-5$. Substitute these values in Quadratic Formula.

$x=\frac{-(-2)\pm \sqrt{(-2{)}^2-4(1\left)\right(-5)}}{2\left(1\right)}$

Step 3. Simplify the value.

On simplification, we get

$\begin{array}{rcl}x& =& \frac{2\pm \sqrt{4+20}}{2}\\ x& =& \frac{2\pm \sqrt{24}}{2}\\ x& =& \frac{2}{2}\pm \frac{2\sqrt{6}}{2}\\ x& =& 1\pm \sqrt{6}\end{array}$

Step 4. Conclusion.

The solutions of the given equation are $x=1\pm \sqrt{6}$.