Question

solve the equation by using any method. rationalize the denominator, if applicabl\\(m^2 + 12m = -2\\)

Explanation:

Step1: Rewrite the equation in standard form

We start with the equation \(m^{2}+12m=-2\). To write it in the standard quadratic form \(ax^{2}+bx + c = 0\), we add 2 to both sides:
\(m^{2}+12m + 2=0\)
Here, \(a = 1\), \(b=12\), and \(c = 2\).

Step2: Use the quadratic formula

The quadratic formula for a quadratic equation \(ax^{2}+bx + c=0\) is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\).
Substituting \(a = 1\), \(b = 12\), and \(c=2\) into the formula:
First, calculate the discriminant \(\Delta=b^{2}-4ac=(12)^{2}-4\times1\times2=144 - 8=136\)
Then, find the roots:
\(m=\frac{-12\pm\sqrt{136}}{2\times1}=\frac{-12\pm2\sqrt{34}}{2}=- 6\pm\sqrt{34}\)

Answer:

\(m=-6+\sqrt{34}\) or \(m=-6 - \sqrt{34}\)