Solve the equation below. List all the solutions. Include all complex solutions.
4x^2−8x+15=0

Step-by-step explanation:

A=4, B=-8, C=15

the discriminant B^2 - 4ac = (-8)^2 - 4(4)(15)

                                  = 64 - 16(15)

                                 = 64 - 240

                                = -176

                           = -1 * 11 * 4 * 4

Since this discriminant is negative, there are two imaginary/complex solutions.

the square root of this discriminant is 4 i sqrt(11)

the two solutions are  [8 +or- 4 i sqrt(11)]/8

                                  = [2 +or- i sqrt(11)]/2

check:

it will suffice to show 4x^2 - 8x = -15        

x^2 = [2 + i sqrt(11)]/4 =  [4 + 4 i sqrt(11)  - 11]/4

                       = [4 i sqrt(11) - 7]/4

then 4x^2 = 4 i sqrt(11) - 7  <--- 4 cancels

and 8x = 4(2 + i sqrt(11) ) <-- 8 cancels 2

        = 8 + 4 i sqrt(11)

So 4x^2- 8x = 4 i sqrt(11) - 7  - [ 8 + 4 i sqrt(11)]

                    = 4 i sqrt(11) - 7 - 8 - 4 i sqrt(11)

                    = -15

which is sufficient to show that the answer is correct.

the two solutions are  [2 +or- i sqrt(11)]/2

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