Final answer:
The quadratic equation 16p²-8p+1=0 can be solved using the quadratic formula by substituting into ax²+bx+c=0, leading to real solutions for the variable 'p'.
Step-by-step explanation:
The equation 16p²-8p+1=0 is a quadratic equation that can be solved for its real solutions using the quadratic formula. The quadratic formula states that for an equation of the form ax²+bx+c=0, the solutions can be found by:
x = (-b ± √(b²-4ac)) / (2a)
In this case, a=16, b=-8, and c=1. Plugging these values into the quadratic formula we can solve for p. First, calculate the determinant √(b²-4ac), which is √((-8)²-4(16)(1)). After computing the determinant, you will get two possible solutions for p by using the plus and minus in the formula. This will provide the real solutions to the equation.