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How To Solve Quadratic Equation by Quadratic Formula

By completing the square the quadratic equation can be made into

$\begin{align}a(x^2+\frac{b}{a}x)&=-c<img src=$ x^2+\frac{b}{a}x&=-\frac{c}{a} (x+\frac{b}{2a})^2&=\frac{b^2}{4a^2}-\frac{c}{a}(x+\frac{b}{2a})^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{align}" border=0 align=absmiddle>

The videos below show you how to practically use the quadratic formula to solve quadratic equation.

How To Solve Quadratic Equation By Completing The Square

Recall that if we have a quadratic equation of the type $x^2=a$ (where $a>0$ ) then the solutions are $x=\pm \sqrt{a}$ .

Now for the general quadratic equation $ax^2+bx+c=0$ we can transform this equation by completing the square into equation of the form $(x+p)^2=q$ . If we think of x+p as one single variable $z$ , then we have $z^2=q$ and this equation is similar to the previous one which we know how to solve it.

The videos below will give you some examples how to do this sort of transformation practically and solve the quadratic equation.

How To Solve Quadratic Equations By Factoring

Any quadratic equation can be written as $ax^2+bx+c=0$ and if factoring the left hand side is possible, we can write the equation as $(ax+p)(x+q)=0$ for some $p$ and $q$ . We can view the last equation as having two numbers that multiply to zero. The only one to have that is if at least one of them is zero (if both of them are not zero then the product is not zero). Thus $ax+p=0$ or $x+q=0$ . From these we can easily solve for $x$ .

These videos will explain to you using a concrete example how to do all of these. If you need to practice your factoring skill, check out this videos first.