SOLUTION: I have to solve this equation by completing the square, and I'm a bit stumped. Any help would be greatly appreciated! 2x^2+10x+11=0 Thank you!

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I have to solve this equation by completing the square, and I'm a bit stumped. Any help would be greatly appreciated! 2x^2+10x+11=0 Thank you!       Log On


   

Question 86430: I have to solve this equation by completing the square, and I'm a bit stumped. Any help would be greatly appreciated!
2x^2+10x+11=0
Thank you!

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use the quadratic formula to solve for x

Starting with the general quadratic

ax%5E2%2Bbx%2Bc

the general form of 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%2B10%2Ax%2B11

x+=+%28-10+%2B-+sqrt%28+%2810%29%5E2-4%2A2%2A11+%29%29%2F%282%2A2%29 Plug in a=2, b=10, and c=11



x+=+%28-10+%2B-+sqrt%28+100-4%2A2%2A11+%29%29%2F%282%2A2%29 Square 10 to get 100



x+=+%28-10+%2B-+sqrt%28+100%2B-88+%29%29%2F%282%2A2%29 Multiply -4%2A11%2A2 to get -88



x+=+%28-10+%2B-+sqrt%28+12+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-10+%2B-+2%2Asqrt%283%29%29%2F%282%2A2%29 Simplify the square root



x+=+%28-10+%2B-+2%2Asqrt%283%29%29%2F4 Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

x+=+%28-10+%2B+2%2Asqrt%283%29%29%2F4 or x+=+%28-10+-+2%2Asqrt%283%29%29%2F4


Which approximate to

x=-1.63397459621556 or x=-3.36602540378444


So our solutions are:
x=-1.63397459621556 or x=-3.36602540378444

Notice when we graph 2%2Ax%5E2%2B10%2Ax%2B11 we get:



when we use the root finder feature on our calculator, we find that x=-1.63397459621556 and x=-3.36602540378444.So this verifies our answer