SOLUTION: Solve the equation by completing the square p2 + 3p

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Question 173413This question is from textbook Introductory Algebra
: Solve the equation by completing the square
p2 + 3p - 9 = 0 This question is from textbook Introductory Algebra

Found 2 solutions by nerdybill, KnightOwlTutor:
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
p^2 + 3p - 9 = 0
p^2 + 3p = 9
Halve the 'b' coefficient (3) to get 3/2 and then square it (9/4)--add to both sides:
p^2 + 3p + 9/4 = 9 + 9/4
(p + 3/2)^2 = 36/4 + 9/4
(p + 3/2)^2 = 45/4
p + 3/2 = sqrt(45/4)
p + 3/2 = (1/2)sqrt(45)
p + 3/2 = (1/2)sqrt(3*3*5)
p + 3/2 = (3/2)sqrt(5)
p = (3/2)sqrt(5) - 3/2
p = 1.8541

Answer by KnightOwlTutor(293) (Show Source):
You can put this solution on YOUR website!
p2 + 3p - 9 = 0.
Add 9 to both sides of the equation
p2 + 3p=9

Divide the coefficient of the p term(=3) term by 2 and square the resultant value and add to both sides of the equation
p2 +3p +(3/2)^2= 9 +(3/2)^2
This makes the quadratic equation a perfect square
(p+3/2)^2=9 +9/4
Simplify the left side of the equation
(p+3/2)^2=36/4+9/4=45/4
(p+3/2)^2=45/4
Take the square root of both sides
p+3/2= + or -3sqrt5/2
subtract 3/2 from both sides
p=-3/2+3sqrt5/2 or p=-3/2-3sqrt5/2

SOLUTION: Solve the equation by completing the square p2 + 3p - 9 = 0