How to derive the general formula for solving quadratic equations

To derive the general formula for solving quadratic equations, follow these steps:
1. Start with the standard form of a quadratic equation: ax² + bx + c = 0, where a, b, and c are constants, and x is the variable.
2. Divide both sides by 'a' to make the coefficient of x² equal to 1: x² + (b/a)x + (c/a) = 0.
3. Move the constant term to the right-hand side: x² + (b/a)x = -c/a.
4. Add (b/2a)² to both sides to complete the square: x² + (b/a)x + (b/2a)² = (b/2a)² - c/a.
5. Factor the left-hand side as a perfect square: (x + b/2a)² = (b/2a)² - c/a.
6. Take the square root of both sides: x + b/2a = ±√((b/2a)² - c/a).
7. Simplify the right-hand side: x + b/2a = ±√(b² - 4ac)/2a.
8. Solve for x by subtracting b/2a from both sides: x = (-b ± √(b² - 4ac))/2a.
This is the general formula for solving quadratic equations, known as the quadratic formula:
x = (-b ± √(b² - 4ac))/2a
Note: This formula works for all quadratic equations, and the ± symbol indicates that there may be two solutions for x.

[@alfredosolari7597]

Thank you sir. A crystal clear explanation. I remember doing quadratic equations as a teenager many years ago. I memorised the general formula, but I never knew where it came from. I just used it like a tool.

[@tambuwalmathsclass]

@@alfredosolari7597 I appreciate it 🙏

[@michaeloviriara3062]

Very true, clever, nice job

[@DotRabbit]

If you rationalise the Quadratic formula you get x= 2c/(-b±√(b²-4ac)) And it works.

[@thisisNishantKr.sharma]

Great explanation sir I am from India 🇮🇳

[@tambuwalmathsclass]

@@thisisNishantKr.sharma Thank you 🙏

[@musasuleman5247]

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[@temitopeolatunde3245]

Great job bro . There is always fact in figure .

[@tambuwalmathsclass]

@@temitopeolatunde3245 🙏🙏🙏

[@Purelyreactions]

🎉🎉

[@LadyCLR]

Off topic: What are your favorite mathematics?

[@tambuwalmathsclass]

@@LadyCLR Calculus

[@Coach_mikkie]

Calculus is my best topic topic

[@LadyCLR]

@@tambuwalmathsclass Wow. Thank you for sharing.

[@blanksonlarbi0808]

Prof

[@tambuwalmathsclass]

@@blanksonlarbi0808 🙏🙏

[@michaeloviriara3062]

It's very clear