SOLUTION: Solve 7x^2 + 5x + 6 = 0 thanks.

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Question 409647: Solve 7x^2 + 5x + 6 = 0
thanks.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

7x%5E2+%2B+5x+%2B+6+=+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 7%2Ax%5E2%2B5%2Ax%2B6=0 ( notice a=7, b=5, and c=6)





x+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A7%2A6+%29%29%2F%282%2A7%29 Plug in a=7, b=5, and c=6




x+=+%28-5+%2B-+sqrt%28+25-4%2A7%2A6+%29%29%2F%282%2A7%29 Square 5 to get 25




x+=+%28-5+%2B-+sqrt%28+25%2B-168+%29%29%2F%282%2A7%29 Multiply -4%2A6%2A7 to get -168




x+=+%28-5+%2B-+sqrt%28+-143+%29%29%2F%282%2A7%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-5+%2B-+i%2Asqrt%28143%29%29%2F%282%2A7%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-5+%2B-+i%2Asqrt%28143%29%29%2F%2814%29 Multiply 2 and 7 to get 14




After simplifying, the quadratic has roots of


x=-5%2F14%2Bsqrt%28143%29%2F14%2Ai or x=-5%2F14-sqrt%28143%29%2F14%2Ai