SOLUTION: x^2-16x+550

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Question 665369: x^2-16x+550
Answer by MathLover1(20850) 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%5E2-16%2Ax%2B550=0 ( notice a=1, b=-16, and c=550)





x+=+%28--16+%2B-+sqrt%28+%28-16%29%5E2-4%2A1%2A550+%29%29%2F%282%2A1%29 Plug in a=1, b=-16, and c=550




x+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%2A1%2A550+%29%29%2F%282%2A1%29 Negate -16 to get 16




x+=+%2816+%2B-+sqrt%28+256-4%2A1%2A550+%29%29%2F%282%2A1%29 Square -16 to get 256 (note: remember when you square -16, you must square the negative as well. This is because %28-16%29%5E2=-16%2A-16=256.)




x+=+%2816+%2B-+sqrt%28+256%2B-2200+%29%29%2F%282%2A1%29 Multiply -4%2A550%2A1 to get -2200




x+=+%2816+%2B-+sqrt%28+-1944+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%2816+%2B-+18%2Ai%2Asqrt%286%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2816+%2B-+18%2Ai%2Asqrt%286%29%29%2F%282%29 Multiply 2 and 1 to get 2




After simplifying, the quadratic has roots of


x=8%2B9%2Asqrt%286%29i or x=8-9%2Asqrt%286%29i