Quadratic Equation Solved

One of the most useful formulas of all time historically is the solution of the equation:
ax² + bx + c = 0.

The equation above is known as the quadratic equation.

Theorem: (-b ± √b² - 4ac)/2a is the solution to the quadratic equation.

(1) First, we multiply both sides by 4a and get:

4a²x² + 4abx + 4ac = 0

(2) Next, we add b² - b² to the equation:

4a²x² + 4abx + b² + 4ac - b² = 0

(3) Now, we add b² - 4ac to both sides which gives us:

4a²x² + 4abx + b² = b² - 4ac

(4) Further, we know that:

(2ax + b)² = 4a²x² + 4axb + b²

(5) Combining #4 and #3, gives us:

(2ax + b)² = b² - 4ac

(6) Now, taking the square root of both sides gives us:

2ax + b = ±√b² - 4ac

(7) Now, using basic algebra, we get to:

x = (-b ±√b² - 4ac)/2a.