Standard form to a quadratic equation? Math people help?

OK, just out of cunfusion





ax^2+bx+c=0 ...standard form





divide all terms by a, so now I have





x^2/a+b/ax+c/a





subract the c/a to the right side so...





x^2+b/ax=-c/a





Now...





x^2+b/ax+(b/2a)^2= -c/a+(b/2a)^2





NOW THE CONFUSION...





(x+b/2a)^2=-c/a+(b/2a)^2...





How do you factor the left side????? What happened here?





Then...





(x+b/2a)^2=b^2-4ac


-------------


4a^2





In the above step, where did the -4ac in the numerator come from? This confused me too!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!...





Then...





x+b/2a=+/- sqrt b^2-4ac/4a^2





Then quadratic form!





I'm sure you do know that!











Thanks so much!

Standard form to a quadratic equation? Math people help?
(x+b/2a)^2=-c/a+(b/2a)^2...


now take the aquare root for both sides and that will give you





x+b/2a=sqr(b^2-4a^2)/2a


x=-b+/-sqr(b^2-4a^2)/2a
Reply:Hi,





ax^2+bx+c=0 ...standard form





divide all terms by a, so now I have





x^2/a+b/ax+c/a





subtract the c/a to the right side so...





x²+b/ax=-c/a





Now...





x²+b/ax+(b/2a)²= -c/a+(b/2a)²





NOW THE CONFUSION...





x²+b/ax+b²/(4a²)= -c/a+b²/(4a²)





The left side always factors into x plus or minus the expression you squared above to complete the square. The sign is the same as what is in front of the x term. That means this factors into:





(x + b/(2a))²





On the right hand side you want to add the fractions together, so you need a common denominator on them.





-c/a+b²/(4a²) =





-c..........b²


----..+..----- Multiply the 1st fraction top and bottom by "4a"


.a........4a²





4a(-c).........b²


---------..+..----- =


4a(a)........4a²





-4ac.....b²


------.+.-----


4a²......4a²





Re-writing this with the positive numerator first, it becomes:





b²-4ac


--------- This is the right side of the equation.


4a²





Now take the square root of both sides. On the left side the square and the square root cancel each other out and leave:





x + b/(2a)





On the right side remember to put a ± in front of the radical.


You can't take the square root of b² - 4ac, so it stays inside the radical sign in the numerator. You can take the square root of 4a² and change the denominator to 2a, without a radical sign.


......______


...../.b² - 4ac


±../.----------- =


..\/.......4a²





I reversed the left and right sides below.


.......______


....\/.b² - 4ac


±..-------------- = x + b/(2a)


...........2a





To get x alone, subtract -b/(2a) on both sides to get:





..........______


-b.±.\/.b² - 4ac


-------------------- = x


.........2a





This is the quadratic formula! I hope this helps!! :-)