4p^2+8p+1=0
Are we solving??
then ...
(2p + 1 )^2 = 0
2p + 1 = 0
2p = -1
p = -1/2
had a mental lapse
4p^2 + 8p + 1 = 0
p = (-8 ± √48)/8
= (-8 ± 4√3)/8
= (-2 ± √3)/2
To find the solution to the equation 4p^2 + 8p + 1 = 0, we can use the quadratic formula. The quadratic formula gives us the solutions to quadratic equations of the form ax^2 + bx + c = 0.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 4, b = 8, and c = 1. Substituting these values into the quadratic formula, we get:
p = (-8 ± √(8^2 - 4*4*1)) / (2*4)
Simplifying further:
p = (-8 ± √(64 - 16)) / 8
p = (-8 ± √48) / 8
p = (-8 ± √(16*3)) / 8
p = (-8 ± 4√3) / 8
Now we can simplify the solutions:
p = (-8 + 4√3) / 8
p = -1 + √3 / 2
p = (-8 - 4√3) / 8
p = -1 - √3 / 2
So the solutions to the equation 4p^2 + 8p + 1 = 0 are:
p = -1 + √3 / 2 and p = -1 - √3 / 2