Question

Solve x2 + 12x = –11 by completing the square. Which is the solution set of the equation? {–11, –1} {–11, 1} {11, –1} {11, 1} , PLEASE HURRY !! :( THANK YOU!

Answer 1

Since quadratic coefient is 1 (term in front of x^2)
take 1/2 of linear cofient (12) and square it
12/2=6, 6^2=36
add that to both sides
x^2+12x+36=-11+36
factor perfect square
(x+6)^2=25
sqrt both sides and take positiv and negative roots
x+6=+/-5
minus 6 both sides
x=-6+/-5
x=-6+5 or x=-6-5
x=-1 or -11

answer is {-11,-1}

Answer 2

Original Equation:

x^2 + 12x = -11

Make it a proper quadratic equation by moving the -11 to the left:

x^2 + 12x + 11 = 0

Find out what 2 numbers multiplied will give us 11 and add up to 12 and break the problem up:

(x + 1)(x + 11) = 0

Now solve for x in both cases:

x+1 = 0
x = -1

x + 11 = 0
x = -11

Your final set is: {-11, -1}