You can put this solution on YOUR website! Given:
.
.
Notice that every term on the left side of this equation has a common factor of 2. Therefore,
we can simplify the equation by dividing both sides (all terms) by 2 to get:
.
.
You can try to factor this, but it doesn't factor nicely. So let's go directly to the quadratic
formula method. This method says that if you have a quadratic equation of the form:
.
.
the solutions for x can be written directly as:
. and
.
.
Notice that by comparing the simplified form of the quadratic equation you were given to
this quadratic formula form, term by term, you know the answers can be directly
figured by
replacing x by m, a by 1, b by +5, and c by +3 in the solution forms.
.
With the appropriate substitutions the solution form:
.
.
becomes:
.
.
And this simplifies to:
.
.
which simplifies even further to:
.
.
Notice that the other solution for m is exactly the same with the exception that the plus
sign between the two terms changes to a minus sign. Therefore, the other solution is:
.
.
I hope that this shows you an understandable way to work quadratic equations using the
quadratic formula to generate the solutions. The quadratic formula is a method that will
work on any quadratic equation.
(