How do you solve 11 + sqrt(2x+1)=2?

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4 Answers
Jan 16, 2018

No solutions.

Explanation:

Our goal is to isolate x so we can find its value.

11+sqrt(2x+1)=2

rArr sqrt(2x+1)=-9

We see that the equation has no solutions because the radical operator over RR always returns positive values. So the equation has no solution.

Jan 16, 2018

The answer is no solution.

Explanation:

Your goal here is to isolate the variable.

First, start by subtracting 2 from both sides, as such:

11-2+sqrt(2x+1)=2-2

9 +sqrt(2x+1) = 0

Then subtract 9 from both sides:

9-9 +sqrt(2x+1) = 0-9

sqrt(2x+1)=-9

Now square both sides:

(sqrt(2x+1))^2=(-9)^2

2x+1=81

Then subtract 1 from both sides:

2x+1-1=81-1

2x=80

Finally, divided both sides by 2:

(2x)/2=80/2

x=40

Plug the answer into the original equation to check if it is correct:

11+sqrt(2(40)+1)=2

11+9=2

20!=2

When plugged in, we can see that x=40 is not correct, so this problem has no solution.

Jan 16, 2018

No Real Solution

Explanation:

Begin by subtracting 11 from both sides

cancel(11color(red)(-11))+sqrt(2x+1)=2color(red)(-11)

sqrt(2x+1)=-9

Square both sides to eliminate the radical on the left side

sqrt(2x+1)^color(red)2=-9^color(red)2

2x+1=81

Subtract 1 from both sides

2x+cancel(1color(red)(-1))=81color(red)(-1)

2x=80

Divide both side by 2

cancel2/cancelcolor(red)2x=80/color(red)2

x=40

However if we verify this by substituting 40 for x in the original expression we'll find:

11+sqrt(2(color(red)40)+1)=2

11+sqrt(81)=2

11+9=2

20!=2

:. There are no real solutions

Jan 19, 2018

No solution for principle root ->+sqrt(2x+1)+11=2

The convention is; that unless the question states
+-sqrt("something") we only use the +sqrt("smething") which is the principle root.

Explanation:

However, just for fun; lets investigate the scenario of (-2)xx(-2)=+4=(+2)xx(+2)

So sqrt(4)=+-2" is definitely viable "ul("only if you ignore the convention")

The convention states : sqrt(4)" can only "=+2" but you need"+-sqrt(4)" to have "+-2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given: sqrt(2x+1)+11=2

Write as +-sqrt(2x+1)+11=2 color(red)(larr" not the actual question")

Subtract 11 from both sides

+-sqrt(2x+1)=-9

Clearly +sqrt(2x+1)=-9 does not have a solution for x in RR as each side of the equals is the opposite sign.

However -sqrt(2x+1)=-9 may have a solution as both sides are negative. Accepting this should not be done as it is against the convention.color(red)(" Note that this is not the question as given")
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Just for fun consider "-sqrt(2x+1)=-9)

Square both sides

2x+1 = +81

2x=80

x=40
Which is not the the answer for the given question as written.

Tony BTony B

The graph clearly shows no solution for +sqrt(2x+1)=-9 which is the answer to the given question as written.

If the question had been +-sqrt(2x+1) then we could legitimately have stated the answer as being: (x,y)->(40,9) is a solution for -sqrt(2x+1)=-9