Question

Can someone please help with this?

Answer 1

Answer:

Answer for x = 5

Step-by-step explanation:

√5x  +11   - 1  = x         We isolate

-√5x+11 = -x-1             We tidy up

√5x+11 = x+1               We raise both sides to second power

  (√5x+11)2 = (x+1)2     After brackets we show after squaring

 5x+11 = x2+2x+1         We rearrange the order

x2  - 3x  -10 = 0           We count the roots = 2

{x1, x2}={5, -2}              We show the roots and show original equation, where the root is isolated, after tidy up

    √5x+11 = x+1           Plug in 5 for  x as x =5

     √5•(5)+11 = (5)+1     Then simplify

     √36 = 6                  Solution checks !!

    Solution is:

     x = 5

Original equation, root isolated, after tidy up

√5x+11 = x+1           Plug in  -2 for  x

√5•(-2)+11 = (-2)+1   Simplify

            √1 = -1        Solution does not check

               1 ≠ -1

Answer for x = 5

Answer 2

Answer:

x= -2, x = 5

Step-by-step explanation:

$\sqrt{5x+11}-1=x$

$\sqrt{5x+11}=x+1$

$5x+11=(x+1)^2$

$5x+11=x^2 + 2x + 1$

$0=x^2 + 2x + 1-5x-11$

$0=x^2 -3x-10$

$0=(x+2)(x-5)$

x= -2, x = 5