Question

Which of the following are solutions to the quadratic equation below?${x}^{2} + 8x = 9$Check all that apply.

Answer 1

Given:

There are given the equation:

$x^2+8x=9$

Explanation:

According to the question:

We need to find the solution to the given quadratic.

Then,

To find the solution, we will use the quadratic equation formula.

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

Then,

From the equation:

$x^2+8x-9=0$

Where,

$a=1,b=8,c=-9$

Then,

Put all the value into the formula:

$\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-8\pm\sqrt{(8)^2-4\times1\times(-9)}}{2\times1} \\ x=\frac{-8\pm\sqrt{64+36}}{2} \end{gathered}$

Then,

$\begin{gathered} x=\frac{-8\pm\sqrt{64+36}}{2} \\ x=\frac{-8\pm\sqrt{100}}{2} \\ x=\frac{-8\pm10}{2} \end{gathered}$

Then,

$\begin{gathered} x=\frac{-8\pm10}{2} \\ x=-\frac{8+10}{2},\frac{-8-10}{2} \\ x=\frac{2}{2},\frac{-18}{2} \\ x=1,-9 \end{gathered}$

Therefore, the solution of the given quadratic equation:

$x=1,-9$

Final answer:

Hence, the correct options are B and E.