Question

Solve by completing the square method: (2/x2 )-(5/x)+2 =0

Answer 1

Answer: x=1/2 or x=2

Step-by-step explanation:

2/x²-5/x+2=0

2-5x+2x²/x²=0

2-5x+2x²=0

2x²-5x+2=0

2x²-4x-x+2=0

2x(x-2)-1(x-2)=0

(2x-1)(x-2)=0

(2x-1)=0 or (x-2)=0

x=1/2 or x=2

Answer 2

Step-by-step explanation:

Solution by completing the square for:

2x2+5x+0=0

Eliminate terms with 0 to get:

2x2+5x=0

a≠1 so divide through by 2

22x2+52x=02

which gives us

x2+52x=0

Take half of the x term and square it

[52⋅12]2=2516

then add the result to both sides

x2+52x+2516=+0+2516

Rewrite the perfect square on the left

(x+54)2=+0+2516

and combine terms on the right

(x+54)2=2516

Take the square root of both sides

x+54=±2516−−−√

Simplify the Radical term (0):

x+54=±54

Isolate the x on the left side and

solve for x (1)

x=−54±54

therefore (3)

x=−54+54

x=−54−54

which becomes

x=0

x=−2.5