SOLUTION: Solve x^2 + 8x + 20 = 0 using the quadratic formula

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Question 456251: Solve x^2 + 8x + 20 = 0 using the quadratic formula
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8x%2B20+=+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=%288%29%5E2-4%2A1%2A20=-16.

The discriminant -16 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 -16 is + or - sqrt%28+16%29+=+4.

The solution is x%5B12%5D+=+%28-8%2B-i%2Asqrt%28+-16+%29%29%2F2%5C1+=++%28-8%2B-i%2A4%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%2B8%2Ax%2B20+%29

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x = -4 ± 2i

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2+%2B+8x+%2B+20+=+0+

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

x+=+%28-8+%2B-+sqrt%28+8%5E2-4%2A1%2A20+%29%29%2F%282%2A1%29+

x+=+%28-8+%2B-+sqrt%28+64-80+%29%29%2F2+

x+=+%28-8+%2B-+sqrt%28-16%29%29%2F2+

x+=+%28-8+%2B-+sqrt%28%28-1%2916%29%29%2F2+

x+=+%28-8+%2B-+4i%29%2F2+

solutions:
x+=+%28-8+%2B+4i%29%2F2+
x+=+-8%2F2+%2B+4i%2F2+
x+=+-4+%2B+2i+
or
x+=+%28-8+-+4i%29%2F2+
x+=+-8%2F2+-+4i%2F2+
x+=+-4+-+2i+

graph:
+graph%28+500%2C+500%2C+-25%2C+25%2C+-25%2C+25%2Cx%5E2+%2B+8x+%2B+20%29+