Rewrite the function by completing the square.
f(x)=x^2-6x+43

x  = 3 ± 2i√13               I think this is right, it's been awhile since I used

                                    complex numbers

Step-by-step explanation:

f(x)=x²-6x+43                              ax² + bx + c = 0

  x²- 6x + 43 = 0

  x²- 6x + ___  = -43                  subtract the constant from both sides  -43

  x²- 6x + -(6/2)²  = -43 + -(6/2)²        add (half of the b coefficent) squared

                                                           to BOTH sides   (6/2)²

 x²- 6x - 9  = -43 - 9

 x²- 6x - 9  = -52

 (x - 3)²  = -52                    now take the square of both sides, oh oh

√ (x - 3)²  = √-52              problem you can't take the square root of a negative

                                          number or can you?

(x - 3)  = √-52                  you have to use "imaginary" numbers to solve this

  x - 3  = i√52                 I am not making this up  √i²52 = i√52  imagine   i² = -1

  x - 3  = ±i√52

      x  = 3 ± 2i√13            there are two imaginary roots I think this is as simple

                                        I can present the answer

           any expression with an "imaginary" part is called a complex number

noncoplanar points are points that do not lie on the same line.

the distance between the school and her home is 3.6km.

12 mins = 0.2 hours = 1/5 hour

54 ÷ 3 = 18km per hour

1/5 of 18 = 3.6km per 12 mins