SOLUTION: When asked to solve the equation (x-3)^2=11, Jess said, "That's easy - just take the square root of both sides," Perhaps Jess also remembered that 11 has two square roots, one posi

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: When asked to solve the equation (x-3)^2=11, Jess said, "That's easy - just take the square root of both sides," Perhaps Jess also remembered that 11 has two square roots, one posi      Log On


   

Question 870895: When asked to solve the equation (x-3)^2=11, Jess said, "That's easy - just take the square root of both sides," Perhaps Jess also remembered that 11 has two square roots, one positive and other negative. What are the two values for x, in exact form? (In this situation, "exact" means no decimals.
(answer= x=3 + square root of 11 and x=3-square root of 11)-----is this correct?
(Continuation) When asked to solve the equation x^2-6x=2, Deniz said, "Hmmm-- not so easy, but I think that adding something to boths sides of the equation is the thing to do," This is indeed a good idea, but what number should Deniz add to both sides? How is this equation related to the previous one?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The first problem is correct.
2. solve the equation x^2 - 6x = 2
This problem can be done easily by "completing the square"
x^2 - 6x + ____ = 2
To find the 3rd term which completes the square:
divide the coefficient of x by 2 and square it; (-6/2)^2 = 9
Add 9 to both sides
x^2 - 6x + 9 = 2 + 9
which is
(x - 3)^2 = 11
look familiar doesn't it
x - 3 = +/-sqrt%2811%29
Two solutions
x = 3 + sqrt%2811%29
and
x = 3 - sqrt%2811%29