SOLUTION: I need help solving this quadratic equation: {{{4x^2+8x+2=0}}}

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I need help solving this quadratic equation: {{{4x^2+8x+2=0}}}      Log On


   

Question 223957: I need help solving this quadratic equation: 4x%5E2%2B8x%2B2=0
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2%2B8x%2B2=0
First, determine whether there is anything common among all three terms -- yes, they all have the common multiple of 2. Therefore, divide both sides by 2 to get:
2x%5E2%2B4x%2B1=0
Since we can't factor, we must resort to the quadratic equation.
Doing so yields:
x = {-0.293, -1.707}
.
Details of the quadratic equation to follow:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%2B1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A2%2A1=8.

Discriminant d=8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+8+%29%29%2F2%5C2+=+-0.292893218813452
x%5B2%5D+=+%28-%284%29-sqrt%28+8+%29%29%2F2%5C2+=+-1.70710678118655

Quadratic expression 2x%5E2%2B4x%2B1 can be factored:
2x%5E2%2B4x%2B1+=+2%28x--0.292893218813452%29%2A%28x--1.70710678118655%29
Again, the answer is: -0.292893218813452, -1.70710678118655. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B1+%29