Quadratic Equation: a*x^2+b*x+c = 0

We all know about quadratic equation. We had solved it many many times in school. Let's recall about quadratic equation.

Quadratic Equation is a second-order polynomial equation in a single variable:

Solutions for x is:

x1 =(-b + sqrt(b^2-4*a*c))/(2*a)

x2 =(-b - sqrt(b^2-4*a*c))/(2*a)

What if we've forgotten the formula ? Let's try to reinvent this formula by ourselves.

1. Subtract left and right part of the equation by c. We will get:

2. Divide both parts by a.

3. (x+y)^2 = x^2 + 2*x*y + y^2. Let's try to transform left part to (x+y)^2.

To be able to do that, add b/(2*a) to both parts of the equation:

4. Open the brackets.

5. Simplify left part to a form (x+y)^2, and make denominators of the right part of the equation the same.

6. Right part can be simplified to:

7. Take the square root of both part:

Why +-sqrt(b^2-4*a*c) ? because (-3)^2 = 9 and 3^2 = 9, that's why :).

8. Subtract b/(2*a) from both parts:

9. The final answer is:

The End.