Question

1. Find the roots of x^2 + 5 = -5x

Answer 1

To find the roots of the equation:

$x^2+5=-5x$

we can use the general formula:

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

First we need to write the equation in the form:

$ax^2+bx+c=0$

Then the equation given takes the form:

$x^2+5x+5=0$

now we identify that a=1, b=5 and c=5. Plugging this values into the general formual we have:

$\begin{gathered} x=\frac{-5\pm\sqrt[]{5^2-4(1)(5)}}{2(1)} \\ =\frac{-5\pm\sqrt[]{25-20}}{2} \\ =\frac{-5\pm\sqrt[]{5}}{2} \end{gathered}$

Hence the roots are:

$\begin{gathered} x=\frac{-5+\sqrt[]{5}}{2} \\ \text{and} \\ x=\frac{-5-\sqrt[]{5}}{2} \end{gathered}$