How do you solve quadratic equations in one variable?

Question

anonymous · Answer

How can you derive the quadratic formula?
How can you solve quadratic equations based on the initial form of the equation?

campbell_st · Answer

the quadratic formula can be derived from completing the square... 

and if the quadratic is in the form

$$ax^2 + bx + c = 0$$

then the formula is 

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

anonymous · Answer

Thank you. Can you help with the other two, I'm just having trouble understanding these three problems

anonymous · Answer

I'll give medals and fan

anonymous · Answer

Can you help with the rest @campbell_st?

campbell_st · Answer

what is the rest..?

anonymous · Answer

The very last question, I found the answer for the first

campbell_st · Answer

my 1st post cover's it... if you know the coefficients a, b and c 

then just substitute and calculate

e.g. 

$$2x^2 + 10x + 3 = 0$$

a = 2, b = 10 and c = 3

so 

$$x = \frac{-10 \pm \sqrt{10^2 - 4 \times 2 \times 3}}{2 \times 2} = \frac{-10\pm \sqrt{76}}{4}$$

and then simplify further

there are 2 answers 

$$x = \frac{-10 + \sqrt{76}}{4}~~~ and ~~~ x = \frac{-10 - \sqrt{76}}{4}$$

anonymous · Answer

This cover's all three questions?