SOLUTION: square root of (x+4)+4=square root of x+20

Algebra.Com
Question 378117: square root of (x+4)+4=square root of x+20
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

Solving equations with variable in a square root:
  1. Isolate a square root.
  2. Square both sides of the equation.
  3. If a square root remains, repeat steps #1 and #2.
  4. The equation should no remaining square roots. Use appropriate techniques to solve the equation.
  5. Check your answer! This is not optional. When you square both sides of an equation (which has been done at least once to get this far), extraneous solutions can appear. Extraneous solutions are solutions that fit the squared equation but do not fit the original equation. Extraneous solution can appear even if no mistakes have been made! This is why the answers must be checked. Any extraneous solutions must be rejected.

Let's see this in action.
1) Isolate a square root. The square root on the right side is already by itself.
2) Square both sides:

The right side is easy to square. But the left side, with its two terms, is not as easy. We need to use FOIL or the pattern , with "a" being and "b" being 4. I like using the pattern:

which simplifies as follows:


3) We still have a square root so we repeat steps #1 and #2:
1) Isolate a square root. Subtracting x and 20 from each side we get:

Dividing both sides by 8 we get:

2) Square both sides:

which gives us:
x+4 = 0
3) The square roots are gone so we can go to step #4
4) Solve the equation. This is a very simple equation to solve. Just subtract 4 from each side:
x = -4
5) Check our solution(s), using the original equation:

Checking x = -4:


0 + 4 = 4
4 = 4 Check!
RELATED QUESTIONS

square root of (x+4)+4=square root of x+20 only x+4 and x+20 is square... (answered by mananth,jsmallt9)
square root of (-4) x square root of... (answered by CharlesG2)
(square root of x) +4=(square root of... (answered by jim_thompson5910)
Square root of... (answered by unlockmath)
A) Square root of 45 x square root of 20 b) Square root of 45 + square root of 20... (answered by Alan3354)
0 = square root of (x-2)... (answered by edjones)
square root of... (answered by Alan3354)
solve square root of 2x=-4 and also square root of x+222-square root of... (answered by swincher4391)
how to solve the square root of x+4= the square root of x plus the square root of... (answered by jsmallt9)