Step 1 :This is a quadratic equation in the form of \(ax^2 + bx + c = 0\). The general solution for such equations is given by the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). In this case, \(a = 1\), \(b = 6\), and \(c = 9\). Let's substitute these values into the quadratic formula to find the solution for \(x\).
Step 2 :Substitute \(a = 1\), \(b = 6\), and \(c = 9\) into the quadratic formula.
Step 3 :Calculate the discriminant \(D = b^2 - 4ac = 0\).
Step 4 :Find the roots of the equation: \(x1 = \frac{-b + \sqrt{D}}{2a} = -3.0\) and \(x2 = \frac{-b - \sqrt{D}}{2a} = -3.0\).
Step 5 :Since both solutions are the same, the equation has one real root at \(x = -3.0\).
Step 6 :Final Answer: The solution to the equation is \(\boxed{x = -3.0}\).