SOLUTION: Solve the quadratic equation for x by the square root: x squared + 8 = 3

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Question 248471: Solve the quadratic equation for x by the square root:
x squared + 8 = 3
Found 2 solutions by College Student, jsmallt9:
Answer by College Student(505) About Me  (Show Source):
You can put this solution on YOUR website!
There is no solution to your problem, unless you are working with imaginary numbers.

x%5E2%2B8=3
x%5E2=3-8
x%5E2=-5

No number multiplied by itself would equal to a negative number, thus there is no solution to this problem.
But, as I said before, if you are working with imaginary numbers, then the answer would be:

x=sqrt%28-5%29 ...which is the same as to say... x=sqrt%285i%29

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming the problem is to solve sqrt%28x%5E2%2B8%29+=+3

To solve for a variable in a square root:
  1. Isolate the square root on sone side of the equation.
  2. Square both sides
  3. Solve the new equation.
  4. Check your answers. This more than just a good idea. It is important because squaring both sides of an equation, like we did in step #2, can introduce what are called extraneous solutions. Extraneous solutions are solutions which work in the squared equation but do not work in the original equation.

1. Isolate the square root. Your square root is already by itself on the left side.

2. Square both sides:
%28sqrt%28x%5E2%2B8%29%29%5E2+=+%283%29%5E2
x%5E2+%2B+8+=+9

3. Solve:
Subtract 9 from each side:
x%5E2+-+1+=+0
Factor:
%28x%2B1%29%28x-1%29+=+0
x+1 = 0 or x=1 = 0
x = -1 or x = 1

4. Check your answers. (Always use the original equation to check.)
Checking x = -1:
sqrt%28%28-1%29%5E2%2B8%29+=+3
sqrt%281%2B8%29+=+3
sqrt%289%29+=+3
3+=+3 Check!
Checking x = 1:
sqrt%28%281%29%5E2%2B8%29+=+3
sqrt%281%2B8%29+=+3
sqrt%289%29+=+3
3+=+3 Check!

(Note: Both answers checked out this time. But don't forrget this step. There will be times when one or more of your solutions are extraneous and muct be rejected.)