SOLUTION: solve in complex number system. x^2-4x+9=0. x to the 2nd power minus 4x plus 9 equals 0

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Question 980627: solve in complex number system. x^2-4x+9=0. x to the 2nd power minus 4x plus 9 equals 0
Found 2 solutions by Boreal, josh_jordan:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
quadratic formula
(1/2a){-b +/- sqrt (b^2-4ac)}
(1/2) {4 +/- sqrt (16-36)} sqrt (-20)= 2i sqrt (5), because it is sqrt (-4)*sqrt (5)
x=(1/2){ 4+/- 2i sqrt (5)}
x=2 +/- i sqrt (5)
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2-4x%2B9%29

Answer by josh_jordan(263) About Me  (Show Source):
You can put this solution on YOUR website!
Because we are dealing with complex numbers, we will need to use the quadratic formula, where a = 1, b = -4, and c = 9, and substitute the letters with the numbers represented by them:

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

x+=+%28-%28-4%29+%2B-+sqrt%28%28-4%29%5E2-%284%29%281%29%289%29%29%29%2F%28%282%29%281%29%29 ----->

x+=+%284+%2B-+sqrt%2816-36%29%29%2F%282%29+ ----->

x+=+%284+%2B-+sqrt%28-20%29%29%2F%282%29+ ----->

x+=+%284+%2B-+2i%2Asqrt%285%29%29%2F%282%29+

Next, factor extract a 2 out of the equation to get rid of the two in our denominator:

x+=+2%282+%2B-+i%2Asqrt%285%29%29%2F%282%29+ ----->

x+=+2+%2B-+i%2Asqrt%285%29+, which is our final answer