SOLUTION: Please help me find the value of X?? {{{((1/2)x)^2+(x)^2=sqrt(5)^2}}}

Algebra ->  Pythagorean-theorem -> SOLUTION: Please help me find the value of X?? {{{((1/2)x)^2+(x)^2=sqrt(5)^2}}}      Log On


   

Question 241255: Please help me find the value of X??
%28%281%2F2%29x%29%5E2%2B%28x%29%5E2=sqrt%285%29%5E2
Answer by College Student(505) About Me  (Show Source):
You can put this solution on YOUR website!
Hello.
.
We know that when we square a square root, they cancel each other...
so... sqrt%285%29%5E2=5
We can now re-write the equation to read:
%28%281%2F2%29x%29%5E2%2Bx%5E2=5
.
We also know that %28%281%2F2%29x%29%5E2=%28x%2F2%29%5E2 right?
So let's square the contents of the parenthesis:
%28x%2F2%29%5E2=%28x%5E2%29%2F%282%5E2%29 thus equal to x%5E2%2F4
.
So we can further simplify the equation to read:
%28x%5E2%2F4%29%2Bx%5E2=5
Let's factor x^2...
x%5E2%28%281%2F4%29%2B%281%29%29=5
Now, convert 1 to a fraction to combine with 1/4
x%5E2%28%281%2F4%29%2B%284%2F4%29%29=5
Add fractions
x%5E2%285%2F4%29=5
Multiply by the fraction's reciprocal on both isides of equation
x%5E2=5%284%2F5%29
The 5 cancels
x%5E2=4
Take square root on both sides to find value of x
x=%2B2or-2
We have two possible solutions x=2 and x=-2