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A Quadratic Equation
is an equation in which the highest power
of an unknown quantity is a square:
ax2+bx+c=0
By the fundamental theorem of algebra, we
know that this equation has two solutions
(but we don’t know if both solutions are
real). Let’s look at some of the methods
used to solve Quadratic Equations:
Solve by factoring
There are numerous methods of factoring,
including greatest
common factor, difference
of squares, and sum
of cubes.
In order to identify which method of factoring
we can apply, we must first set up the equation
to solve for 0. Here’s an example:
-6 =3-4x2
First, let’s move all of the terms from
the right side of the equation to the left,
so that the equation is set up to solve
for 0.
-6-3+4x2=3-4x2-3+4x2
-6-3+4x2=0
Now we have the expression set equal to
0. Next, let’s simplify the left side of
the equation:
4x2-9=0
With the equation simplified, we can identify
this expression as a difference
of squares. We can factor using the
difference of squares formula:
x2-y2= (x+y)(x-y)
Factor the expression:
4x2-9=(2x+3)(2x-3)=0
(2x+3)(2x-3)=0
The next step in solving a quadratic equation
is to set each factor equal to zero.
2x+3=0
2x-3=0
Finally, solve each equation.
2x+3=0
2x=-3
x=-3/2
2x-3=0
2x=3
x=3/2
So the two solutions for x are -3/2 and
3/2.
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