Brainliest if first 5 minutes. Solve the equation using inverse operations. Check your solutions. In your final answer, include all of your work.

1/4x^3 = -27/4

x= -

2

/3 = −27  =  2

/3−3i  =3  =1.5000−2.5981i

x=  2

/3+  −27

=  2

/3+3i/3  = 1.5000+2.5981i

x=−3

Step by Step Explanation:

5.6     Solving    x2-3x+9 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =    -3

                     C   =   9

Accordingly,  B2  -  4AC   =

                    9 - 36 =

                    -27

Applying the quadratic formula :

              3 ± √ -27

  x  =    —————

                   2

In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written  (a+b*i)  

Both   i   and   -i   are the square roots of minus 1

Accordingly,√ -27  =  

                   √ 27 • (-1)  =

                   √ 27  • √ -1   =

                   ±  √ 27  • i

Can  √ 27 be simplified ?

Yes!   The prime factorization of  27   is

  3•3•3  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 27   =  √ 3•3•3   =

               ±  3 • √ 3

 √ 3   , rounded to 4 decimal digits, is   1.7321

So now we are looking at:

          x  =  ( 3 ± 3 •  1.732 i ) / 2

Two imaginary solutions :

x =(3+√-27)/2=(3+3i√ 3 )/2= 1.5000+2.5981i

 or:  

x =(3-√-27)/2=(3-3i√ 3 )/2= 1.5000-2.5981i

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step-by-step explanation:

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