Question

Solve the equation by completing the square.
x^2 + 18x +70 = 0

Answer 1

Man, it's been a while since I've completed squares.
What we're going to do is move the +70 to the other side, so it looks like
x^2 + 18x + __ = -70 + __ (these blanks are for when we complete the square!)
now, we take half of the coefficient before the x and square it, and then put it into the blank on both sides.
so 1/2 of 18 is 9
9^2 = 81
x^2 + 18x + 81 = -70 + 81
x^2 + 18x + 81 = 11
then, we factor the left side
(x + 9)(x + 9) = 11 OR (x + 9)^2 = 11
so
(x + 9)^2 = 11
take the square of both sides
x + 9 = +/- sqrt(11)
x = 9 +/- sqrt(11)
(because of the +/-, you will have two answers! this is because we took the square root!)

Answer 2

x^2+18x=-70
x^2+18x+81=-70+81
(x+9)^2=11
Darn It he beat me to it lol

Answer 3

Sorry! I get excited about completing squares!

Answer 4

isn't it - 9 +- sqrt 11? because u -9 from x+9

Answer 5

Ooh, yeah. You're right!

Answer 6

is x^2 = sqrt of 11 equal to x= +- sqrt of 11? or is it just +-11?

Answer 7

Man, it's been a while since I've completed squares.
What we're going to do is move the +70 to the other side, so it looks like
x^2 + 18x + __ = -70 + __ (these blanks are for when we complete the square!)
now, we take half of the coefficient before the x and square it, and then put it into the blank on both sides.
so 1/2 of 18 is 9
9^2 = 81
x^2 + 18x + 81 = -70 + 81
x^2 + 18x + 81 = 11
then, we factor the left side
(x + 9)(x + 9) = 11 OR (x + 9)^2 = 11
so
(x + 9)^2 = 11
take the square of both sides
x + 9 = +/- sqrt(11)
x = 9 +/- sqrt(11)
(because of the +/-, you will have two answers! this is because we took the square root!)