Quadratic equations can be solved in 3 different ways.
1.
Factoring Method. (Remember that not every math problem can be factored, thus the quadratic formula or complete the square methods should be
used instead.)
Set the equation to equal 0: ax2+bx+c=0
All like terms should be combined to one side in the equation and x2 should be kept positive.
The following example is from udemy.com
2x2-8x-4=3x-x2
Here we have to solve for x, but first as I said before, all the like terms should be grouped together and the squared term should be kept positive.
2x2+x2-8x-3x-4=0
If possible, the terms should be grouped together even more by adding the like terms, for example 2x2+x2=3x2, -8x-3x=-11x, the completed equation should look like
this:
3x2-11x-4=0
The next step is to factor
(3x+1)(x-4)=0
The next step is to find a combination that results in -11x
When multiplying the equation above we get
3x2-12x+x-4, by further simplification we get -11x.
Next step solving.
3x+1=0;
-1=0-1; 3x=-1; 3x/3=-1/3
x-4=0; -4=0-4; x=-4; x=-1/3
x equals -1/3 and -4.
2.
Quadratic Method or Formula.
A quadratic equation looks like this in standard form: x2 – 4x – 7 = 0. Quad means squared, so we know
that the quadratic equation must have a squared term, or it isn’t quadratic. The other numbers and