SOLUTION: Solve for x If the solutions are complex numbers, then give soulutions in the usual a + bi form a) x^2 - 6x + 9 = 0 b) x^2 + 4x + 7 = 0

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Question 191307: Solve for x
If the solutions are complex numbers, then give soulutions in the usual a + bi form
a) x^2 - 6x + 9 = 0
b) x^2 + 4x + 7 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)



x%5E2-6x%2B9=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-6, and c=9


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%289%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-6, and c=9


x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%289%29+%29%29%2F%282%281%29%29 Negate -6 to get 6.


x+=+%286+%2B-+sqrt%28+36-4%281%29%289%29+%29%29%2F%282%281%29%29 Square -6 to get 36.


x+=+%286+%2B-+sqrt%28+36-36+%29%29%2F%282%281%29%29 Multiply 4%281%29%289%29 to get 36


x+=+%286+%2B-+sqrt%28+0+%29%29%2F%282%281%29%29 Subtract 36 from 36 to get 0


x+=+%286+%2B-+sqrt%28+0+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%286+%2B-+0%29%2F%282%29 Take the square root of 0 to get 0.


x+=+%286+%2B+0%29%2F%282%29 or x+=+%286+-+0%29%2F%282%29 Break up the expression.


x+=+%286%29%2F%282%29 or x+=++%286%29%2F%282%29 Combine like terms.


x+=+3 or x+=+3 Simplify.


So solution is x+=+3


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b)



x%5E2%2B4x%2B7=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=4, and c=7


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%284%29+%2B-+sqrt%28+%284%29%5E2-4%281%29%287%29+%29%29%2F%282%281%29%29 Plug in a=1, b=4, and c=7


x+=+%28-4+%2B-+sqrt%28+16-4%281%29%287%29+%29%29%2F%282%281%29%29 Square 4 to get 16.


x+=+%28-4+%2B-+sqrt%28+16-28+%29%29%2F%282%281%29%29 Multiply 4%281%29%287%29 to get 28


x+=+%28-4+%2B-+sqrt%28+-12+%29%29%2F%282%281%29%29 Subtract 28 from 16 to get -12


x+=+%28-4+%2B-+sqrt%28+-12+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-4+%2B-+2i%2Asqrt%283%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-4%29%2F%282%29+%2B-+%282i%2Asqrt%283%29%29%2F%282%29 Break up the fraction.


x+=+-2+%2B-+sqrt%283%29%2Ai Reduce.


x+=+-2%2Bsqrt%283%29%2Ai or x+=+-2-sqrt%283%29%2Ai Break up the expression.


So the answers are x+=+-2%2Bsqrt%283%29%2Ai or x+=+-2-sqrt%283%29%2Ai where i=sqrt%28-1%29

Note: the solutions are in the form x=a%2Bbi or x=a-bi where a=-2 and b=sqrt%283%29