Question

In the following exercises, solve by using the Quadratic Formula.
$(x+2)(x+6)=21$

Short answer

The solutions of the given equation are $x=1$and $x=-9$.

Step-by-step solution

Step 1. Write the quadratic equation in standard form.

The given equation is:

$(x+2)(x+6)=21$

The given equation can be written as:

$\begin{array}{rcl}{x}^2+6x+2x+12& =& 21\\ x^2+8x+12-21& =& 0\\ x^2+8x-9& =& 0\end{array}$

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, $a=1,b=8,c=-9$. Substitute these values in Quadratic Formula.

$x=\frac{-8\pm \sqrt{(8{)}^2-4(1\left)\right(-9)}}{2\left(1\right)}$

Step 3. Simplify the value.

On simplification, we get

$\begin{array}{rcl}x& =& \frac{-8\pm \sqrt{64+36}}{2}\\ x& =& \frac{-8\pm \sqrt{100}}{2}\\ x& =& \frac{-8}{2}\pm \frac{10}{2}\\ x& =& -4\pm 5\end{array}$

It can be written as:

$\begin{array}{rcl}x& =& -4+5\text{and}x=-4-5\\ x& =& 1\text{and}x=-9\end{array}$

Step 4. Conclusion.

The solutions of the given equation are $x=1$and $x=-9$.