Problem

$9 x^{2}-12 x+4=0$

Answer

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Answer

\(\boxed{x = \frac{2}{3}}\)

Steps

Step 1 :Given the quadratic equation: \(9x^2 - 12x + 4 = 0\)

Step 2 :Using the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) where a = 9, b = -12, and c = 4

Step 3 :Calculate the discriminant: \(D = b^2 - 4ac = (-12)^2 - 4(9)(4) = 0\)

Step 4 :Since the discriminant is 0, there is only one real solution for x

Step 5 :Calculate the solution: \(x = \frac{-(-12) \pm \sqrt{0}}{2(9)} = \frac{12}{18} = \frac{2}{3}\)

Step 6 :\(\boxed{x = \frac{2}{3}}\)

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