SOLUTION: sqrt(8x+49)-sqrt(2x+28)=3

Question 1010099: sqrt(8x+49)-sqrt(2x+28)=3
Found 2 solutions by MathLover1, addingup:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

solutions:

since will make in negative radicand which will give us complex zero, we will take only as a solution

Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
sqrt(8x+49)-sqrt(2x+28)=3 Square both sides to get rid of sqrt
77+10x-2sqrt((2x+28)(8x+49))= 9
Subtract 10 x+77 from both sides:
-2sqrt((2x+28)(8x+49))= -68-10x
Raise both sides to the power of two:
4(2x+28)(8x+49)= (-68-10x)^2 On the left, FOIL
64x^2+1288x+5488= (-68-10x)^2 Square numbers on right (and remember that -10^2= -10*-10= 100, in other words, -*- = +)
64x^2+1288x+5488 = 100x^2+1360x+4624
Subtract 100x^2+1360x+4624 from both sides:
64x^2+1288x+5488 = 100x^2+1360x+4624
-
100x^2+1360x+4624= 100x^2+1360x+4624
------------------------------------
-36x^2-72x+864= 0 Let's factor the left side:
-36(x-4)(x+6)= 0 Now simplify by dividing both sides by -36 (and remember that 0 divided by any number = 0, so the right doesn't change)
(x-4)(x+6)= 0
x-4= 0 or x+6= 0
x= 4 or x= -6
Try each one of these in the equation to see which one makes the equation true. I've already done a lot of typing so you can do it on your own. You'll find that 4 is the correct answer.
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