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

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

sqrt%288x%2B49%29-sqrt%282x%2B28%29=3+
%28sqrt%288x%2B49%29-sqrt%282x%2B28%29%29%5E2=3%5E2+

8x%2B49-2sqrt%28%282x%2B28%29%288x%2B49%29%29%2B2x%2B28=9+
10x%2B77-2sqrt%28%282x%2B28%29%288x%2B49%29%29=9+
10x%2B77-9=2sqrt%28%282x%2B28%29%288x%2B49%29%29+
10x%2B68=2sqrt%28%282x%2B28%29%288x%2B49%29%29+
%2810x%2B68%29%5E2=%282sqrt%28%282x%2B28%29%288x%2B49%29%29%29%5E2+
100x%5E2%2B1360x%2B4624=4%2816x%5E2%2B322x%2B1372%29+
100x%5E2%2B1360x%2B4624=64x%5E2%2B1288x%2B5488+
100x%5E2%2B1360x%2B4624-64x%5E2-1288x-5488=0+
%28100x%5E2-64x%5E2%29%2B%281360x-1288x%29%2B%284624-5488%29=0+
36x%5E2%2B72x-864=0+
36x%5E2%2F36%2B72x%2F36-864%2F36=0+
x%5E2%2B2x-24=0+
x%5E2%2B6x-4x-24=0+
%28x%5E2%2B6x%29-%284x%2B24%29=0+
x%28x%2B6%29-4%28x%2B6%29=0+
%28x-4%29%28x%2B6%29+=+0
solutions:
x=4
x=-6
since x=-6 will make in sqrt%288x%2B49%29 negative radicand which will give us complex zero, we will take only highlight%28x=4%29 as a solution



Answer by addingup(3677) About Me  (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.