SOLUTION: Solve the quadratic equation by completing the square: 2x^2 + 10x + 11 = 0 Can someone please explain to me the idea behind the quadratic equation, thank you

Algebra ->  Equations -> SOLUTION: Solve the quadratic equation by completing the square: 2x^2 + 10x + 11 = 0 Can someone please explain to me the idea behind the quadratic equation, thank you      Log On


   

Question 65770: Solve the quadratic equation by completing the square:
2x^2 + 10x + 11 = 0
Can someone please explain to me the idea behind the quadratic equation, thank you
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
A quadratic equation is one in which the highest power of the independent variable (x in this case) is 2. Quadratic comes from the latin "Quadra" meanining square.
Solve by completing the square:
2x%2A2+%2B10x+%2B+11+=+0 First,divide through by 2 in order to get the coefficient of x%5E2 = 1.
x%5E2+%2B+5x+%2B+11%2F2+=+0 Next, subtract 11/2 from both sides.
x%5E2+%2B+5x+=+-11%2F2 Now add to both sides, the square of half the coefficient of x. This is:%285%2F2%29%5E2+=+25%2F4
x%5E2+%2B+5x+%2B+25%2F4+=+%2825%2F4%29-11%2F2 Now simplify this.
%28x%2B5%2F2%29%5E2+=+3%2F4 Take the square root of both sides.
x%2B5%2F2+=+sqrt%283%2F4%29 The sqrt%283%2F4%29 will have a + or - in front of it. Subtract 5%2F2 from both sides.
x+=+%28-5%2F2%29%2B-sqrt%283%2F4%29
The solutions are:
x+=+%28-5%2Bsqrt%283%29%29%2F2 = -1.63397 (Approx.)
x+=+%28-5-sqrt%283%29%29%2F2 = -3.36603 (Approx.)