Problem

a) $x^{2}-14 x+24=0$

Answer

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Answer

\(\boxed{x1 = 12, x2 = 2}\)

Steps

Step 1 :Given the quadratic equation: \(x^{2}-14 x+24=0\)

Step 2 :Use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Step 3 :Identify the coefficients: \(a = 1\), \(b = -14\), and \(c = 24\)

Step 4 :Calculate the discriminant: \(\Delta = b^2 - 4ac = 100\)

Step 5 :Find the solutions: \(x1 = \frac{-(-14) + \sqrt{100}}{2(1)} = 12\) and \(x2 = \frac{-(-14) - \sqrt{100}}{2(1)} = 2\)

Step 6 :\(\boxed{x1 = 12, x2 = 2}\)

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