SOLUTION: solve using the quadratic formula {{{x^2-4x+40=0}}}

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Question 872005: solve using the quadratic formula x%5E2-4x%2B40=0
Found 2 solutions by ben720, richwmiller:
Answer by ben720(159) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-4x%2B40=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A40+%29%29%2F%282%2A1%29+
x+=+%284+%2B-+sqrt%28+16-160+%29%29%2F%282%29+
x+=+%284+%2B-+sqrt%28+-144+%29%29%2F%282%29+
You cannot find the square root of a negative number.

NO SOLUTIONS

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
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%5E2-4%2Ax%2B40=0 ( notice a=1, b=-4, and c=40)





x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A40+%29%29%2F%282%2A1%29 Plug in a=1, b=-4, and c=40




x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A40+%29%29%2F%282%2A1%29 Negate -4 to get 4




x+=+%284+%2B-+sqrt%28+16-4%2A1%2A40+%29%29%2F%282%2A1%29 Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because %28-4%29%5E2=-4%2A-4=16.)




x+=+%284+%2B-+sqrt%28+16%2B-160+%29%29%2F%282%2A1%29 Multiply -4%2A40%2A1 to get -160




x+=+%284+%2B-+sqrt%28+-144+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%284+%2B-+12%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+=+%284+%2B-+12%2Ai%29%2F%282%29 Multiply 2 and 1 to get 2




After simplifying, the quadratic has roots of


x=2%2B6%2Ai or x=2-6%2Ai