You can
put this solution on YOUR website!You are correct.
"Subtracting a squared number from 68" translates as
where
is the mystery number, and "doubling the number" would be
, just as you wrote.
You could also write your quadratic equation as
, or even as
(equivalent equations).
COMPLETING THE SQUARE:
Since
reminds me of
, I would be tempted to "complete the square" by just adding 1 to each side of the equal sign in that last equation.
-->
-->
The solutions would be
and -->
Then we could subtract 1 from each side of the equal sign in the equations above to get
and -->
which can be summarized as
USING THE QUADRATIC FORMULA:
The other option is using the quadratic formula. Any equation of the form
has as solutions
.
That formula is called the quadratic formula.
From the values for the coefficient (a, b, and c) in any quadratic equation, you can find the solutions using that formula
If
the solutions are not real numbers, so if the only numbers you know are real numbers, then you say there are no solutions.
(By the way, the expression
is called the discriminant).
Plugging those values into the quadratic formula, any computer can solve a quadratic equation.
(Humans have more trouble because they tend to make mistakes in their calculations).
To apply the quadratic formula, if you start with
you have
,
and
.
Plugging those values into the quadratic formula, you have
-->
-->
-->
-->
-->
-->
-->
(I feel tempted to write the plus sign on the bottom in
above,
to show that it was on the top before multiplying times (-1), but the order does not matter, and the symbol I can write has the plus on top).
