## anonymous 5 years ago when do we use quadratic formula ? Can we use it whenever we want or there are special conditions when we use them ?

1. anonymous

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

2. anonymous

expression=0 right side has to =0

3. anonymous

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.

4. anonymous

$x^2+6x-1=0$ 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

5. anonymous

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

6. anonymous

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