SOLUTION: solve the equation for complex solutions x^2-6x+25=0 is the answer 6(+-)8i/2 or do I need to reduce to 3(+-)4i or am I wrong all together

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Question 779350: solve the equation for complex solutions
x^2-6x+25=0
is the answer 6(+-)8i/2 or do I need to reduce to 3(+-)4i or am I wrong all together
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-6x+25=0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B25+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-6%29%5E2-4%2A1%2A25=-64.

The discriminant -64 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -64 is + or - sqrt%28+64%29+=+8.

The solution is x%5B12%5D+=+%28--6%2B-i%2Asqrt%28+-64+%29%29%2F2%5C1+=++%28--6%2B-i%2A8%29%2F2%5C1+, or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B25+%29

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x = 3(+-)4i

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-6x%2B25=0..use quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+... .note: a=1, b=-6, and c=25

x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A25+%29%29%2F%282%2A1%29+

x+=+%286+%2B-+sqrt%2836-100%29%29%2F2+
x+=+%286+%2B-+sqrt%28-64%29%29%2F2+
x+=+%286+%2B-+8i%29%2F2+
x+=+6%2F2+%2B-+8i%2F2+
x+=+3+%2B-+4i+
solutions:
x+=+3+%2B+4i+
x+=+3+-+4i+