Question 1047961
.
Find the real solutions of the equation. 

The long square root is covering x^2-x-4=x+5
 What is the solution set?
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Notice: It is much better to use parentheses than the word descriptions in math.
It is proved more than 2000 years history.


Parentheses are free !!
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<pre>
{{{sqrt(x^2-x-4)}}} = x+5.

Square both sides. You will get

{{{x^2 - x - 4}}} = {{{(x+5)^2}}}.

Simplify

{{{x^2 -x -4}}} = {{{x^2 + 10x + 25}}},

0 = 11x + 29,

11x = - 29,

x = {{{-29/11}}}.

Can you check it?
</pre>

I better will illustrate it graphically.

<TABLE> 
  <TR>
  <TD> 

{{{graph( 330, 330, -5.5, 5.5, -1.5, 6.5,
          sqrt(x^2-x-4), x+5
)}}}


Plots y = {{{sqrt(x^2-x-4)}}} (red) and y = x+5 (green).

  </TD>
  </TR>
</TABLE>