Question

when do we use quadratic formula ? Can we use it whenever we want or there are special conditions when we use them ?

Answer 1

you can always use the quadratic formula for solving a quadratic equation.

Answer 2

expression=0
right side has to =0

Answer 3

completing the square is usually easiest when the leading coefficient is 1 and the 'middle term' has even coefficient, like the example \[x^2+4x=21\]
the quadratic equation forces a denominator on you which is often unnecessary.
factoring is easiest but only works if the problem is cooked up to factor, like in an elementary algebra text.

Answer 4

\[x^2+6x-1=0\] via completing the square:
\[x^2+6x=1\]
\[(x+3)^2=1+3^2=10\]
\[x+3=\sqrt{10}\] or
\[x+3=-\sqrt{10}\]
done

Answer 5

ok not done.
\[x=-3+\sqrt{10}\]
\[x=-3-\sqrt{10}\]

Answer 6

now by quadratic formula:
a = 1, b = 6, c = -1
\[x= \frac{-6 + \sqrt{6^2-4\times 1 \times -1}}{2}\]
\[x=\frac{-6 + \sqrt{36+4}}{2}\]
\[x=\frac{-6 + \sqrt{40}}{2}\]
\[x=\frac{-6 + \sqrt{4\times10}}{2}\]
\[x=\frac{-6 +2 \sqrt{10}}{2}\]
\[x=\frac{2(-3 + \sqrt{10})}{2}\]
\[x=-3+\sqrt{10}\]
what a pain