Question

Solve the equation (Completing the Square) x^2+7x+6=0

Answer 1

To complete the square, do the following:

1. Put equation in the form ax^2 + bx = c

x^2 + 7x = -6

2. Add (b/2)^2 to both sides:

(7/2)^2 = 49/4

x^2 + 7x + 49/4 = -6 + 49/4

3. Simplify the left side into a perfect square:

(x + 7/2)^2 = -6 + 49/4

4. Simplify the right side of the equation:

(x+7/2)^2 = -24/4 + 49/4
(x+7/2)^2 = 25/4

Take the square root of both sides:
x + 7/2 = + or - 5/2

Isolate x:

x = -5/2 - 7/2 = -12/2 = -6
x = 5/2 - 7/2 = -2/2 = -1

x = (-6,-1)

Answer 2

Thank you!(: