Help √ (x+2) + √(3x+7) = 1?

Question

√ (x+2) + √(3x+7) = 1

i got

15±√137
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4

i dont think that it is correct

is there anyway that that is correct or am i totally wrong... if you say i am wrong can you please tell how you got the other answer thank you

Answer 1

I didn't get 4
First of all, the square root of 137 isn't correct.
15 plus the square root would be somewhere around 26.
Get it right for me!!!!!

Answer 2

(1) Square both sides of that equation.
(2) Substract from the resulting squared equation the first and last terms you get from squaring the left side of that equation. Simplify. You are now left with a square root expression on the left and an expression consisting of X and integers on the right.
(3) Square that equation again. You should get a quadratic expression on both sides.
(4) Simplify that equation to the form 0=aX^2+b^X+c
(5) Solve for X by the quadratic formula. You should get -1 and -2.
(6) Double check the validity of the original equation with the two answers you got by putting X=-1 and X=-2 into the equation.

Yes, X=-1 does work. There are actually 4 different expressions you can write when you put X=-1 into your original equation (remember both positive and negative roots). One of them is true.

Answer 3

One way to check you answer is to put one of the values in for x and see if the original statement is true...
I got x = -1 or -2...

You would have to move one of the Sq. Roots to the other side and then square both sides... after squaring (remember on side would require the FOIL method) then simply and you are still left with one square root- keep that by itself on one side and again square both sides to get rid of the final sq. root. You need to be careful with negative signs when foiling ans squaring.
Hope this helps!

Answer 4

square both sides
then (x+2) + (3x+7) =1
4x+9=1
4x=-8
x=-2