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
am I on the right track here?
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
am I on the right track here?
First, be careful with your parentheses! Most people would read "1 + or - sqrt -27/2" as $\displaystyle 1\pm\sqrt{\frac{-27}{2}}$ but what you mean is $\displaystyle \frac{1\pm\sqrt{27}}{2}$ which, without LaTex, should be written as (1 + or - sqrt(27))/2.
Now, for the square root: $\displaystyle \sqrt{-27}= \sqrt{(-1)(27)}= \sqrt{-1}\sqrt{27}$. The square root of -1 is, by definition, "i". So $\displaystyle \sqrt{-27}= i\sqrt{27}$. It is also true that 27= 9(3) so $\displaystyle \sqrt{27}= \sqrt{9}\sqrt{3}= 3\sqrt{3}$. Your teacher might insist that you write the answer as $\displaystyle \frac{1\pm 3i\sqrt{3}}{2}$ and, in any case, it is better to do so.