Question

Root. 2x square -5x +root 2=0

Answer 1

Answer:

csc

( 2 x ) + √ 2 = 0

Explanation:

Subtract  

√ 2

from both sides of the equation.

csc

( 2 x ) = − √ 2

Take the inverse cosecant of both sides of the equation to extract  

x

from inside the cosecant.

2 x = arccsc ( − √ 2 ) The exact value of  arccsc ( − √ 2 )  is  − π 4 . 2 x = − π 4 Divideeachterm by  

2  and simplify.

Tap for more steps... x = − π 8

The cosecant function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from  

2 π , to find a reference angle. Next, add this reference angle to  

π  to find the solution in the third quadrant.

2 x = 2 π + π 4 + π=  0

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Answer 2

Answer:

csc

( 2 x ) + √ 2 = 0

Explanation:

Subtract  

√ 2  

from both sides of the equation.  

csc  

( 2 x ) = − √ 2  

Take the inverse cosecant of both sides of the equation to extract    

x  

from inside the cosecant.  

2 x = arccsc ( − √ 2 ) The exact value of  arccsc ( − √ 2 )  is  − π 4 . 2 x = − π 4 Divideeachterm by    

2  and simplify.

Tap for more steps... x = − π 8  

The cosecant function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from    

2 π , to find a reference angle. Next, add this reference angle to  

π  to find the solution in the third quadrant.

2 x = 2 π + π 4 + π=  0

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