SOLUTION: 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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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?

Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
.
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 !!
--------------------------

sqrt%28x%5E2-x-4%29 = x+5.

Square both sides. You will get

x%5E2+-+x+-+4 = %28x%2B5%29%5E2.

Simplify

x%5E2+-x+-4 = x%5E2+%2B+10x+%2B+25,

0 = 11x + 29,

11x = - 29,

x = -29%2F11.

Can you check it?

I better will illustrate it graphically.



Plots y = sqrt%28x%5E2-x-4%29 (red) and y = x+5 (green).