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Solve the equation p^2 + 4p = 1 by completing the square.

Show your work.

First, add 1 to both sides of the equations

take the coefficient of p, which is 4, divide by 2, giving 2, and finally square it giving 4.

second, add 4 to both sides of the equation to get p^2+4p+4=5

adding 4 has completed the left hand side into a perfect square:

p^2+4p+4 =

(p+2) * (p+2) =

(p+2) ^2

things which are equal to the same thing are also equal to each other since

p^2+4p+4 = 5 and

p^2+4p+4 = (p+2) ^2

then, according to the law of transitivity,

(p+2) ^2 = 5

now, taking the square roots of both sides, we get

p+2 = √ 5

Since a square root has two values, one positive and the other negative

p2 + 4p - 1 = 0

has two solutions:

p = - 2 + √ 5

or

p = - 2 - √ 5