You can
put this solution on YOUR website! Solve sqrt(5x+1) +2 = 2x
sqrt(5x+1) = 2x - 2,
Squaring both sides: 5x + 1 = 4(x-1)^2 = 4x^2 -8x +4.
Or 4x^2 - 13x + 3 =0,
Factoring: (x-3)(4x -1) = 0,
So,x = 3 or 1/4
Check, when x =3, sqrt(5*3+1) +2 = sqrt(16) + 2 = 4+2 = 6
= 2*3 =6 (right)
when x =1/4, sqrt(5/4+1) +2 = sqrt(9/4) + 2 = 3/2 + 2 = 7/2
= 2 * 1/4 - 2 = -3/2 (invalid, ignore, it is
the redundant root obtained by taking square)
Answer: The only roor is x= 3.
You can
put this solution on YOUR website!
You'll first want to subtract 2 from both sides of the equation so as to isolate the square root.
Next, square both sides to eliminate the square root.
You'll next want to move all of your terms to one side of the equation. Do this by subtracting 5x and 1 from both sides.
Combine like terms to get
. This quadratic can be factored into
. So either
or
. After solving both equations, you'll get that x=(1/4) or 3.
To check your answers, plug both (1/4) and 3 back into the original problem. Checking 3 first, we see that
Notice that this is equivalent to the other side of the equation
. So this answer checks.
But notice that (1/4) does not check when you plug it back into the original problem:
and the other side of the equation gives us that
.
That means that this equation has only one solution x=3.
(I didn't see the other solution that looks just like this, so sorry for the redundancy. I only saw the first incomplete solution. =) )
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