SOLUTION: quadratic formula 2xsquared + 5x + 11=0

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Question 129448: quadratic formula
2xsquared + 5x + 11=0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2+%2B+5x+%2B+11=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 2%2Ax%5E2%2B5%2Ax%2B11=0 ( notice a=2, b=5, and c=11)





x+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A2%2A11+%29%29%2F%282%2A2%29 Plug in a=2, b=5, and c=11




x+=+%28-5+%2B-+sqrt%28+25-4%2A2%2A11+%29%29%2F%282%2A2%29 Square 5 to get 25




x+=+%28-5+%2B-+sqrt%28+25%2B-88+%29%29%2F%282%2A2%29 Multiply -4%2A11%2A2 to get -88




x+=+%28-5+%2B-+sqrt%28+-63+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-5+%2B-+3%2Ai%2Asqrt%287%29%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-5+%2B-+3%2Ai%2Asqrt%287%29%29%2F%284%29 Multiply 2 and 2 to get 4




After simplifying, the quadratic has roots of


x=-5%2F4%2B3%2Asqrt%287%29%2F4%2Ai or x=-5%2F4-3%2Asqrt%287%29%2F4%2Ai