SOLUTION: May I have some help with this expression? Find all solutions of the equation and express them in the form a + bi. x^2 + 12x + 37 = 0

Algebra ->  Equations -> SOLUTION: May I have some help with this expression? Find all solutions of the equation and express them in the form a + bi. x^2 + 12x + 37 = 0      Log On


   

Question 120458: May I have some help with this expression?
Find all solutions of the equation and express them in the form a + bi.
x^2 + 12x + 37 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve x%5E2%2B12%2Ax%2B37=0 ( notice a=1, b=12, and c=37)




x+=+%28-12+%2B-+sqrt%28+%2812%29%5E2-4%2A1%2A37+%29%29%2F%282%2A1%29 Plug in a=1, b=12, and c=37



x+=+%28-12+%2B-+sqrt%28+144-4%2A1%2A37+%29%29%2F%282%2A1%29 Square 12 to get 144



x+=+%28-12+%2B-+sqrt%28+144%2B-148+%29%29%2F%282%2A1%29 Multiply -4%2A37%2A1 to get -148



x+=+%28-12+%2B-+sqrt%28+-4+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-12+%2B-+2%2Ai%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-12+%2B-+2%2Ai%29%2F%282%29 Multiply 2 and 1 to get 2



After simplifying, the quadratic has roots of

x=-6+%2B+i or x=-6+-+i