Expert Answers
hala718 eNotes educator| Certified Educator

sqrt(x^2 + 5) = x+2

First let us square both sides:

==> x^2 + 5 = (x+2)^2

Now open brackets:

==> x^2 + 5 = x^2 + 4x + 4

Now reduce similar:

==> 5 = 4x + 4

==> Now subtract  4:

==>  1 = 4x

Divide by 4:

==> 1/4 = x

==> x = 1/4

giorgiana1976 | Student

Before starting to solve any equation that contains square root, we have to impose constraints of existence of square roots.

In our case, the expression under the square root, has to be positive or equal to zero.

The expression under the square root is:

x^2 +5 >=0

It is obvious that for any value of x, positive or negative, the expression x^2 +5 is always positive, so the square root equation could be solved.

The first step in solving the equation is to remove the square root, so, we'll square raise both side of the equality:

[sqrt(x^2 +5)]^2 = (x+ 2)^2

We'll expand the square from the right side:

x^2 +5 = x^2 +4x + 4 

We'll eliminate lke terms:

5 = 4x + 4

We'll isolate 4x to the right side:

5-4 = 4x

1 = 4x

We'll divide by 4:

x = 1/4

neela | Student

To solve sqrt(x^2+5) = x+2.

Solution:

Squaring both sides of the equation, we get:

x^2+5 = (x+2)^2

x^2+5 = x^2+4x+4

 0 = x^2+4x+4-x^2-5

0 =  4x-1

4x -1 = 0 gives x = 1/4.

Access hundreds of thousands of answers with a free trial.

Start Free Trial
Ask a Question