1) p + 14 p - 38 = 0

Add 38 to both sides of the equation.

p2+14p=38

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b.

(b/2) 2 = (7) ^2

Add the term to each side of the equation.

p^2 + 14p + (7) 2=38 + (7) 2

Simplify the equation.

p^2 + 14p + 49 = 87

Factor the perfect trinomial square into (p+7) ^2

(p+7) 2=87

Solve the equation for p.

p = ± √87 - 7

Take the square root of each side of the equation to set up the solution for

p:

(p+7) 2 ⋅ 12 = ±√87

Remove the perfect root factor p + 7 under the radical to solve for p.

p + 7 = ±√87

Subtract

7

from both sides of the equation.

p = ±√87 - 7

Exact Form:

p = ±√87 - 7

Decimal Form:

p = 2.32737905