How do you solve #x^(2) - 10x + 24=0#?

Find 2 numbers, knowing sum (-b = 10) and product (c = 24). Factor pairs of (24) -->... (3, 8)(4, 6). This sum is 10. Then, the 2 real roots are: 4 and 6

Hopefully this helps!

To solve the equation (x^2 - 10x + 24 = 0), you can use the quadratic formula: (x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}), where (a), (b), and (c) are the coefficients of the quadratic equation (ax^2 + bx + c = 0). For this equation, (a = 1), (b = -10), and (c = 24). Substituting these values into the quadratic formula gives you (x = \frac{{10 \pm \sqrt{{(-10)^2 - 4(1)(24)}}}}{{2(1)}}). Simplifying under the square root gives (x = \frac{{10 \pm \sqrt{{100 - 96}}}}{2}), which further simplifies to (x = \frac{{10 \pm \sqrt{4}}}{2}). Thus, (x = \frac{{10 \pm 2}}{2}). This results in two solutions: (x = 6) and (x = 4). Therefore, the solutions to the equation (x^2 - 10x + 24 = 0) are (x = 6) and (x = 4).