Question

Please help!! What Find the Error and explain why it is wrong!

Answer 1

First image attached

The error was done in Step E, because student did not multiply
`2\cdot x -8` by the negative sign in numerator. Step E must be
`(2\cdot x -5)/((x+4)\cdot (x-4))`.

Second image attached

The error was done in Step C, because the student omitted the
`2\cdot a \cdot b` of the algebraic identity
`(a+b)^(2) = a^(2)+2\cdot a\cdot b +b^(2)`. Step C must be
`5\cdot x = x^(2)+4\cdot x + 4`

Explanation:

First image attached

The error was done in Step E, because student did not multiply
`2\cdot x -8` by the negative sign in numerator. The real numerator in Step E should be:

`3-(2\cdot x -8)= 3-2\cdot x+8 = 11-2\cdot x`

Hence, Step E must be
`(2\cdot x -5)/((x+4)\cdot (x-4))`.

Second image attached

The error was done in Step C, because the student omitted the
`2\cdot a \cdot b` of the algebraic identity
`(a+b)^(2) = a^(2)+2\cdot a\cdot b +b^(2)`. Step C must be
`5\cdot x = x^(2)+4\cdot x + 4`

And further steps are described below:

Step D

`x^(2)-x+4 = 0`

Which according to the Quadratic Formula, represents a polynomial with complex roots. That is: (
`a = 1`,
`b = -1`,
`c = 4`)

`D = b^(2)-4\cdot a\cdot c`

`D = (-1)-4\cdot (1)\cdot (4)`

`D = -17` (Conjugated complex roots)

Step E

`(x-0.5-i\,1.936)\cdot (x-0.5+i\,1.936) = 0`

Step F

`x = 0.5+i\,1.936\,\lor\,x = 0.5-i\,1.936`