Question

find the exact solution for this equation by completing the square:
ax^2+bx+c=0

Answer 1

Just "unexpand" the quadratic formula to find this in reverse.\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]Start by multiplying both sides by \(2a\), adding \(b\) to both sides, squaring both sides, etc.

Answer 2

i still dont understand

Answer 3

Once you can get that formula that I wrote into \(ax^2+bx+c=0\) by manipulating things, just write the steps in reverse. That formula is derived by completing the square, and will be the ultimate result of completing the square and solving for \(x\). It's just a lot easier to do this in my opinion over trying to complete the square of \(ax^2+bx+c=0\) and do things in the "correct" order.

Answer 4

okay.. i kinda understand it...

Answer 5

Any question?

Answer 6

the one i wrote down at the top..i dont quite understand her method..i was taught to solve using completing the squares

Answer 7

...

Answer 8

\[a x^2+b x +c=0\]

\[x^2+\frac{b}{a}x+\frac{c}{a}=0\]

\[\left(x+\frac{b}{2a}\right)^2=\frac{b^2}{4a^2}-\frac{c}{a}\]

\[\left(x+\frac{b}{2a}\right)^2=\frac{b^2-4 a c}{4 a^2}\]

\[\frac{b}{2 a}+x=\pm \sqrt{\frac{b^2-4 a c}{4 a^2}}\]

\[x=\pm \sqrt{\frac{b^2-4 a c}{4 a^2}}-\frac{b}{2 a}\]

\[x=\frac{\pm \sqrt{b^2-4 a c}}{2a}-\frac{b}{2 a}\]

Answer 9

\[x=\frac{-b\pm \sqrt{b^2-4 a c}}{2a}\]

Answer 10

WOAHH!!! that makes so much more sense..omg..thank u soooo much imran!!!!

Answer 11

I just posted; this fast?

Answer 12

well..it was simple the whole time, its ezactly the quatratic equation..i jus needed sumbody to write it...lols