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Solving equations by the quadratic formula
In 8.1, we discussed the quadratic formula as a method of
solving quadratic equations. It can be
used on any quadratic equation . The quadratic formula is actually a derivation
of completing the
square and its final form looks like this :
Ex. 1
Solve by using the quadratic formula:
*You might want to start off by reminding yourself what a,
b, and c stand for: Now put those into
the quadratic formula :
Work under the radical first and be sure to use the order of
operations : . Keep working under
the radical: Simplify the radical if
possible and calculate the answers :
*Before starting this problem, put the equation in
descending order and set the equation equal to zero :
Now use the quadratic formula :
Again, work under the
radical and use the order of operations to get :
We can’t take the square root of 8
evenly and remember that the square root of a negative
number is imaginary so we’ll simplify it this way:
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