SOLUTION: solve square root of 2x=-4 and also square root of x+222-square root of x+46=8

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Question 442311: solve square root of 2x=-4 and also square root of x+222-square root of x+46=8
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
If I understand correctly your two problems are:
1) sqrt%282x%29+=+-4
2) sqrt%28x%2B222%29+-+sqrt%28x%2B46%29+=+8
For number 1, remember that to "undo" square roots, we need to square both sides.
Thus, we have , then our answer would be x+=+8i.
For number 2, let's multiply by the conjugate.

x%2B222+-+x%2B46++=+8%28sqrt%28x%2B222%29+%2B+sqrt%28x%2B46%29%29
176+=+8%28sqrt%28x%2B222%29+%2B+sqrt%28x%2B46%29%29
22+=+sqrt%28x%2B222%29+%2B+sqrt%28x%2B46%29%29
recall that +8=sqrt%28x%2B222%29+-+sqrt%28x%2B46%29
Then 22+=+sqrt%28x%2B222%29+%2B+sqrt%28x%2B46%29
8+=+sqrt%28x%2B222%29+-+sqrt%28x%2B46%29
if we add the two equations we get:
30 = 2sqrt(x+222)
15 = sqrt(x+222)
225 = x+222
x =3.
if we subtract the two equations we get:
14 = 2sqrt(x+46)
7 = sqrt(x+46)
49 = x + 46
x=3
So, x+=+3