$x^{2}+6 x+8$
Final Answer: The solutions to the equation \(x^{2}+6 x+8 = 0\) are \(x = \boxed{-4.0}\) and \(x = \boxed{-2.0}\).
Step 1 :We are given the quadratic equation \(x^{2}+6 x+8 = 0\).
Step 2 :This is a quadratic equation in the form of \(ax^2 + bx + c\).
Step 3 :To solve this equation, we can use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
Step 4 :Here, \(a = 1\), \(b = 6\), and \(c = 8\).
Step 5 :Substituting these values into the quadratic formula, we get the solutions \(x = -4.0\) and \(x = -2.0\).
Step 6 :These are the values of \(x\) that satisfy the equation \(x^{2}+6 x+8 = 0\).
Step 7 :Final Answer: The solutions to the equation \(x^{2}+6 x+8 = 0\) are \(x = \boxed{-4.0}\) and \(x = \boxed{-2.0}\).