Step 1 :Given the quadratic equation: \(x^2 - 12x + 36 = 0\)
Step 2 :Using the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Step 3 :Substitute the values: \(a = 1\), \(b = -12\), and \(c = 36\)
Step 4 :Calculate the discriminant: \(\Delta = b^2 - 4ac = (-12)^2 - 4(1)(36) = 144 - 144 = 0\)
Step 5 :Since the discriminant is 0, there is only one solution: \(x = \frac{-b + \sqrt{\Delta}}{2a} = \frac{12 + \sqrt{0}}{2(1)} = \frac{12}{2} = 6\)
Step 6 :\(\boxed{x = 6}\)