## anonymous 5 years ago What would be the most logical first step to solve this quadratic equation? x2+2x+13=8

1. anonymous

what level is this? (that equation only has imaginary roots and, without stereotyping, most people who know about imaginary numbers can solve quadratics)

2. anonymous

just use ur quadtratic equatin and substitute.

3. anonymous

so would it be the square root of both sides .

4. anonymous

is it x^2?

5. anonymous

Did you make up this question yourself?

6. anonymous

no its algebra twilight math class .

7. anonymous

its not complicated, just put in the quadtratic formula, the values of Ax +Bx +C=0, where in ur case, its x^2 +2x +5 =0..... or am i missing something...

8. anonymous

Hmm. Well the first step would be to either set it to 0, or complete the square. It won't factorise, so I'd complete the square. But you'll still need to square root a negative number.

9. anonymous

i dont know how to do that sorry im not qood at math worse subject evr .

10. anonymous

Note $\sqrt{-1} = i$

11. anonymous

where do u see a negative value?

12. anonymous

nvm is see it now...

13. anonymous

{ -2 ± Sq Root ( 4 - 20 ) } / 2

14. anonymous

unless u use imaginary numbers, thats as simplified as it gets...

15. amistre64

subtract the right hand side from both sides of the equation would be the first step

16. amistre64

x2+2x+13 -8=8 -8 x^2 +2x +5 = 0

17. amistre64

the next step would be to "complete the square".... if you dont know the quadratic formula that is :) x^2 +2x +5 = 0 ; subtract 5 from both sides x^2 +2x + ___ = -5 + ____ we need to find a suitable number to fill in these blanks with; we need to create a "perfect" square trinomial that will factor into: (x+?)^2 we know that the product of a binomial and itself is: (a+b)(a+b) = a^2 +2ab + b^2 what we have is: a^2 +a(2__ ) + (___)^2

18. anonymous

I know the quadratic formula, but would still complete the square.

19. amistre64

if I recall correctly, completing the sqaure is how we get the quadratic formula :)

20. anonymous

Affirmative.

21. anonymous

lol.

22. anonymous

man im in university calc, and i dont even remember how to complete the square...havent done that since 9th grade haha

23. amistre64

(a+b)(a+b) = a^2 +2ab + b^2 what we have is: a^2 +a(2__ ) + (___)^2 we see that if we divide the midde term by 2a we will get a suitable "b" right? x^2 +2x +5 ....2x/2x = 1...b=1 b^2 = 1

24. anonymous

pellet, university calc. That's harcore.

25. anonymous

hardcore* :@

26. amistre64

x^2 +2x +1 = -5+1 (x+1)^2 = -4 already see a problem lol x+1 = +-sqrt(-4) x = -1 +- sqrt(-4)

27. anonymous

its also really hard, and i dont know why i need it if im in software engineering, but ok...

28. anonymous

Because Maths is everything.

29. amistre64

x = -1 +- 2i :) but thats a complex number and not a "real" number

30. anonymous

$x^2 + 2x + 13 = 8$ $\iff (x+1)^2 = -4$ $\implies (x+1) = \pm \sqrt{-4} = \pm \sqrt{-1}\sqrt{4} = \pm 2i$ $\implies x = -1 \pm 2i$

31. anonymous

sorry had that typed out but realised you were explaining it so waited - but didn;t want all that typing to go to waste.

32. amistre64

lol ..... you did good ;)

33. amistre64

does that make any sense miranda?

34. anonymous

... :(

35. anonymous

im sure thats a yes ;)