SOLUTION: solve: sqrt of x+5 + sqrt of x-3 = 4

Question 255553: solve: sqrt of x+5 + sqrt of x-3 = 4
Found 2 solutions by EMStelley, edjones:
Answer by EMStelley(208) (Show Source): You can put this solution on YOUR website!

When you are solving a problem with two square roots, you always want to start by rearranging the formula to have one square root on each side:

Now we square both sides:

Now, we combine like terms and isolate the one remaining square root:

And now we square both sides again:

The last step is to check our answer:

So x=4 is a valid solution.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
sqrt(x+5)+sqrt(x-3)=4
x+5+2sqrt(x+5)sqrt(x-3)+x-3=16 square each side.
2sqrt(x+5)sqrt(x-3)=14-2x
sqrt(x+5)sqrt(x-3)=7-x
(x+5)(x-3)=x^2-14x+49 square each side.
x^2+2x-15=x^2-14x+49
16x-64=0
16x=64
x=4
.
Ed
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