Answer:
p = -7 ±√87
Explanation:
p2+14p-38=0 would be clearer if written as p^2+14p-38=0: use " ^ " for exponentiation.
Let's "complete the square" to solve this quadratic equation:
Taking half of the coefficient of the p term, which is 14, yields 7.
Squaring this result yields 49.
Add this 49 to p^2 + 14p and also add 49 to the right side, obtaining:
p^2 + 14p + 49 - 38 = 49
Rewriting p^2 + 14p + 49 as a perfect square, we get:
(p + 7)^2 = 87
Let's now find p. Take the square root of both sides, obtaining
p + 7 = ±√87
Isolate p by subtracting 7 from both sides:
p = -7 ±√87
These are the "solutions" or "roots" or "zeros" of p^2+14p-38=0.