Could someone check my work please? 2 algebra probs?

Question

This is my first semester back to college math, so I need all the help I can get.... (x^2 = x squared and i^2 = i squared)

:)

0.015v^2 + v + 10

a. where v=30 mph

0.015(30)2 + 30 + 10

0.015(900) + 40

13.5 + 40

a. answer: 53.5

b.where v=55 mph

0.015(55)2 + 55 + 10

0.015 (3025) + 65

45.375

b. answer: 110.375

If x=1- 2i, then x2 -2x + 5=0

(1+2i)(1+2i) - 2(1+2i) + 5=0

1 + 2i + 2i + 4i^2 - 2 - 4i + 5=0

1 + 4i + 4(-1) - 2 - 4i + 5=0

1 - 4 - 2 + 5=0

-3 - 2 + 5=0

-5 + 5=0

0=0

Thank you

Answer 1

I haven't had to do math like that for 20 years.  Now my brain hurts.

Answer 2

a - correct

b - correct

c - wrong; you used (1 + 2i) instead of (1 - 2i) which I re-wrote as (1 + -2i)

(1 + -2i)(1 + -2i) + -2(1 + -2i) + 5 = 0

1 + -2i + -2i + 4i^2 + -2 + 4i + 5 = 0

1 + -4i + 4i^2 + -2 + 4i + 5 = 0  ***-4i + 4i = 0***

1 + 4i^2 + -2 + 5 = 0

4i^2 + 4 = 0

4(i^2 + 1) = 0

4(i + 1)(i - 1) = 0

~~~~~~but I don't remember where to go from there.....