Final answer:
To solve x²-10x+16>0, we factor the quadratic to (x-2)(x-8)>0. The inequality is satisfied when x<2 or x>8. We don't need the quadratic formula in this case because the quadratic can be easily factored.
Step-by-step explanation:
To solve the inequality x²-10x+16>0, we look for values of x for which the quadratic expression is positive. We can do this by factoring the quadratic, if possible, or using the quadratic formula to find the roots of the corresponding equation x²-10x+16=0.
Factoring the quadratic expression, we get (x-2)(x-8)>0. This product is greater than zero when either both factors are positive, which happens for x>8, or when both factors are negative, which happens for x<2. Hence, our solution is x<2 or x>8.
It's important to check the signs of the intervals determined by the roots. In this case:
- For x<2, both (x-2) and (x-8) are negative, which makes their product positive.
- For 2
- For x>8, both (x-2) and (x-8) are positive, which makes their product positive.
Therefore, the complete solution to the inequality x²-10x+16>0 is the set of all x values such that x is less than 2 or x is greater than 8.