SOLUTION: Solve the following quadratic equations by factoring or by any other techniques of this chapter and explain why you chose that method over the other methods or each problem. {{

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve the following quadratic equations by factoring or by any other techniques of this chapter and explain why you chose that method over the other methods or each problem. {{      Log On


   

Question 74839This question is from textbook Beginning Algebra
: Solve the following quadratic equations by factoring or by any other techniques of this chapter and explain why you chose that method over the other methods or each problem.
%28x-1%29%5E2=7
The answer I got was 2sqrt%287%2B1%29. I am not sure what method I used and why or how to explain it. I am needed some help with that part. Is this answer correct? Thanks This question is from textbook Beginning Algebra

Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28%28x-1%29%5E2%29=0%2B-sqrt%287%29Take the square root of both sides
x%2Bcross%28-1%2B1%29=0%2B-sqrt%287%29%2B1Add 1 to both sides
So x equals
x=0%2B-sqrt%287%29%2B1note: ignore the zero


Check:
%28%28sqrt%287%29%2B1%29-1%29%5E2=7Plug in x=sqrt%287%29%2B1
%28sqrt%287%29%29%5E2=7
7=7works
%28%28-sqrt%287%29%2B1%29-1%29%5E2=7Plug in x=-sqrt%287%29%2B1
%28-sqrt%287%29%29%5E2=7
7=7works


Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
%28x-1%29%5E2+=+7 Take the square root of both sides.
x-1+=+sqrt%287%29 or x-1+=+-sqrt%287%29 In both cases, add 1 to both sides.
x+=+1%2Bsqrt%287%29 or x+=1-sqrt%287%29 These are the roots.
This uses the square root method becuase it is most direct.