SOLUTION: Can somebody help me find x: {{{((1/2)x)^2+(x)^2=sqrt(5)^2}}}

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Question 251828: Can somebody help me find x: %28%281%2F2%29x%29%5E2%2B%28x%29%5E2=sqrt%285%29%5E2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Take note that %28sqrt%285%29%29%5E2=sqrt%285%29%2Asqrt%285%29=sqrt%285%2A5%29=sqrt%2825%29=5. So %28sqrt%285%29%29%5E2=5. Also, keep in mind that %28%281%2F2%29x%29%5E2=%281%2F4%29x%5E2


%28%281%2F2%29x%29%5E2%2B%28x%29%5E2=%28sqrt%285%29%29%5E2 Start with the given equation.


%281%2F4%29x%5E2%2Bx%5E2=5 Square the individual terms (see above).


%285%2F4%29x%5E2=5 Combine like terms (this just amounts to adding fractions).


5x%5E2=5%2A4 Multiply both sides by 4.


x%5E2=%285%2A4%29%2F5 Divide both sides by 5.


x%5E2=%28cross%285%29%2A4%29%2Fcross%285%29 Cancel out the common terms.


x%5E2=4 Simplify.


x=%22%22%2B-sqrt%284%29 Take the square root of both sides.


x=sqrt%284%29 or x=-sqrt%284%29 Break up the "plus/minus" to form two equations.


x=2 or x=-2 Take the square root of 4 to get 2.


x=2 or x=-2 Combine like terms.


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Answer:


So the solutions are x=2 or x=-2.