SOLUTION: what is the solution set of the quadratic equation 8x2 + 2x + 1 = 0

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Question 418360: what is the solution set of the quadratic equation 8x2 + 2x + 1 = 0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

8x%5E2+%2B+2x+%2B+1+=+0

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 8%2Ax%5E2%2B2%2Ax%2B1=0 ( notice a=8, b=2, and c=1)





x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A8%2A1+%29%29%2F%282%2A8%29 Plug in a=8, b=2, and c=1




x+=+%28-2+%2B-+sqrt%28+4-4%2A8%2A1+%29%29%2F%282%2A8%29 Square 2 to get 4




x+=+%28-2+%2B-+sqrt%28+4%2B-32+%29%29%2F%282%2A8%29 Multiply -4%2A1%2A8 to get -32




x+=+%28-2+%2B-+sqrt%28+-28+%29%29%2F%282%2A8%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-2+%2B-+2%2Ai%2Asqrt%287%29%29%2F%282%2A8%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-2+%2B-+2%2Ai%2Asqrt%287%29%29%2F%2816%29 Multiply 2 and 8 to get 16




After simplifying, the quadratic has roots of


x=-1%2F8%2Bsqrt%287%29%2F8%2Ai or x=-1%2F8-sqrt%287%29%2F8%2Ai