Somewhere else in this group, FT029 wrote:

"I tried my wrath with the quadratic formula. I failed. Puzzle: 2x squared + 2x + 1 = 0 I got 0.5675, and that's way off... My simplest form was -2 - root 20 / 4, and I rounded that to the hundreth. What did I do wrong..."

Quadratic formula:

The solution(s) to the equation ax^2 + bx + c = 0 are given by: x = [-b +- squareroot(b^2 - 4ac)] / 2a.

a, b, c are coefficients. So in your example, 2x^2 + 2x + 1 = 0, the values of a, b, c are a = 2, b = 2, c = 1.

Solutions: x = [-2 +- squareroot (2^2 - 4(2)(1))] / 2(2).

Simplifying, x = [-2 +- squareroot (-4)] / 4.

Since we have the squareroot of a negative number, it means we can stop here and conclude that there is no solution. That is, no solution within the "real numbers".

If we go outside the real numbers into the "imaginary numbers" then we can continue simplifying:

x = [-2 +- 2i] / 4

x = -2/4 +- 2i/4

x = -1/2 +- (1/2) i.

x = -1/2 + (1/2)i or x = -1/2 - (1/2)i

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