Solve for x

Question

x + 5 = √x+5   + 6

 

the x+5 is all under the root

 

√3x+10  - 4 = x

the 3x+10 is all under the root

 

√2x+1  + √x = √5x+5

 

Answer 1

I will only answer the first one for you.  Then apply what you learn to answer the other two.

 

1)

 

x + 5 = √(x + 5) + 6

 

 

Isolate the radical term by subtracting 6 to both sides of the equation.

 

x - 1 = √(x + 5)

 

 

Square both sides of the equation to undo the radical term.

 

(x - 1)(x - 1) = x + 5

 

x² - 2x + 1 = x + 5

 

 

Move all terms to the left side of the equation to make the right equal to zero.

 

x² - 3x - 4 = 0

 

 

You now have a quadratic equation.  Solve this quadratic equation for x.  Then check each x value by plugging it into the original equation to see which solution works out.

Answer 2

Hanna, I'll do the first. If you want to show what all is under the radical, put it in parentheses, like √(x + 5) + 6

 

x + 5 = √(x + 5) + 6

x - 1 = √(x + 5)

 

Square both sides!

 

(x - 1)² = x + 5

x² - 2x + 1 = x + 5

x² - 3x - 4 = 0

(x - 4)(x + 1) = 0

 

x - 4 = 0

     x = 4

 

x + 1 = 0

       x = -1

 

Hope this helps!