SOLUTION: PLEASE HELP ME! √x+7-4=4 the answer in the book is 57. how??

Algebra ->  Radicals -> SOLUTION: PLEASE HELP ME! √x+7-4=4 the answer in the book is 57. how??      Log On


   

Question 383577: PLEASE HELP ME! √x+7-4=4 the answer in the book is 57. how??
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%2B7%29-4+=+4
Start by isolating the square root (by adding 4 to each side):
sqrt%28x%2B7%29+=+8
Square both sides of the equation (to eliminate the square root):
%28sqrt%28x%2B7%29%29%5E2+=+%288%29%5E2
which simplifies to:
x + 7 = 64
And the subtract 7 from each side:
x = 57

Solving equations with square roots usually involves squaring both sides of the equation. (We did so in this problem.) And when you square both sides of any equation you should check your answers. This is important because squaring both sides can introduce what are called extraneous solutions. Extraneous solutions are solutions that fit the squared equation but do not fit the original equation! So we must check to make sure the solution we found actually works in the original equation. And we should use the original equation to check:
sqrt%28x%2B7%29-4+=+4
Checking x = 57:
sqrt%28%2857%29%2B7%29-4+=+4
sqrt%2864%29-4+=+4
8-4 = 4
4 = 4 Check!