Mahesh Godavarti
-1
Quadratic formula is derived using "completing the square" as shown below: \begin{array}{lllr} ax^2 + bx + c &=& 0 &\\ x^2 + \frac{b}{a} x + \frac{c}{a} &=& 0 & \text{dividing both sides by } a \\ x^2 + 2 \frac{b}{2a} x + \left(\frac{b}{2a}\right)^2 - \left(\frac{b}{2a}\right)^2 + \frac{c}{a} &=& 0 &\\ \left(x + \frac{b}{2a} \right)^2 &=& \frac{b^2 - 4ac}{4a^2} & \\ x + \frac{b}{2a} &=& \pm \frac{\sqrt{b^2 - 4ac}}{2a} &\\ x &=& \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} & \end{array}
Craig Young
0
This solution lost the x term in the third line.
Mahesh Godavarti
0
You are correct! Fixing it.
Mahesh Godavarti
0
Fixed it. Hopefully, it's correct now.