Eallorise \( x^{2}-10 x+16 \)

To solve the quadratic equation \( x^2 - 10x + 16 = 0 \), we can use the quadratic formula, which is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a = 1 \), \( b = -10 \), and \( c = 16 \). Plugging these values in, we get: 1. Calculate the discriminant: \( b^2 - 4ac = (-10)^2 - 4(1)(16) = 100 - 64 = 36 \). 2. Find the roots: \( x = \frac{10 \pm \sqrt{36}}{2(1)} = \frac{10 \pm 6}{2} \). This gives us the solutions \( x = 8 \) and \( x = 2 \). Voilà! You've just factored the equation without needing to factor by hand—easy peasy! Quadratic equations like this one are not just for math class; they show up everywhere in real life! Ever wondered how projectile motion is calculated? Or how to determine the optimal price for maximum profit? These equations help model situations involving trajectories, inventory, marketing strategies, or even in architecture for structural stability—so mastering them really pays off!