SOLUTION: {{{1+3^""/x^""}}}{{{""=""}}}{{{28^""/x^2}}} solve by completing square method

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Question 1101649: 1%2B3%5E%22%22%2Fx%5E%22%22%22%22=%22%2228%5E%22%22%2Fx%5E2 solve by completing square method

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
1%2B3%5E%22%22%2Fx%5E%22%22%22%22=%22%2228%5E%22%22%2Fx%5E2

Multiply through by x2

x%5E2%2B3x%22%22=%22%2228

Multiply 3 by 1%2F2, get 3%2F2
Square 3%2F2, get 9%2F4
Add 9%2F4 to both sides:

x%5E2%2B3x%2B9%2F4%22%22=%22%2228%2B9%2F4

Factor the left side:
Get LCD of 4 on the right side:

%28x%2B3%2F2%29%28x%2B3%2F2%29%22%22=%22%2228%2Aexpr%284%2F4%29%2B9%2F4

Write the left side as the square of a binomial since 
both factors are the same.
Multiply the 28 by the numerator 4 on the right side.

%28x%2B3%2F2%29%5E2%22%22=%22%22112%2F4%2B9%2F4

Finish combining the right side:

%28x%2B3%2F2%29%5E2%22%22=%22%22121%2F4

Take square roots of both sides, remembering ±
on the right side.

sqrt%28%28x%2B3%2F2%29%5E2%29%22%22=%22%22%22%22+%2B-+sqrt%28121%2F4%29

x%2B3%2F2%22%22=%22%22%22%22+%2B-+11%2F2

Use the + on the right

x%2B3%2F2%22%22=%22%2211%2F2

Subtract 3%2F2 from both sides:

x%22%22=%22%2211%2F2-3%2F2 

x%22%22=%22%228%2F2

x%22%22=%22%224  <-- that's one solution.

Go back to 

x%2B3%2F2%22%22=%22%22%22%22+%2B-+11%2F2

Use the - on the right

x%2B3%2F2%22%22=%22%22-11%2F2

Subtract 3%2F2 from both sides:

x%22%22=%22%22-11%2F2-3%2F2 

x%22%22=%22%22-14%2F2

x%22%22=%22%22-7  <-- that's the other solution.

The solution set is {-7,4}

Edwin