quadratic formula

[Handicap Joe]

Use the quadratic formula to solve the equation

x^2 - x = -7
x^2 - x + 7 = -7 + 7
x^2 - x + 7 = 0
a=1, b=-1,c=-7
-(-1) + or - sqrt(-1)^2-4(1)(7) / 2(1)
1 + or - sqrt 1-28 / 2
1 + or - sqrt -27/2
if this is correct so far My problem is finding the complex roots, can someone direct me?

 

[Aladdin]

Use the quadratic formula to solve the equation

x^2 - x = -7
x^2 - x + 7 = -7 + 7
x^2 - x + 7 = 0
a=1, b=-1,c=-7... c= +7
-(-1) + or - sqrt(-1)^2-4(1)(7) / 2(1)
1 + or - sqrt 1-28 / 2
1 + or - sqrt -27/2
if this is correct so far My problem is finding the complex roots, can someone direct me?

 

[Denis]

1 + or - sqrt -27/2
if this is correct so far My problem is finding the complex roots, can someone direct me?

Correct; start showing these PROPERLY: x = [1 +- sqrt(-27)] / 2

sqrt(-27) = sqrt(9 * 3 * -1) = 3sqrt(3 * -1) = 3sqrt(3)sqrt(-1) = 3sqrt(3)i : i = sqrt(-1)
So:
x = [1 +- 3sqrt(3)i] / 2

That's all you need. If you want to find out more on i = sqrt(1), go here:

http://staff.jccc.net/swilson/complex/imagnumbers.htm