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paisley13
22.05.2021 •
Mathematics
A quadratic equation is shown below: x2 − 8x + 13 = 0 Which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers? (5 points) Subtract 5 from both sides of the equation Subtract 3 from both sides of the equation Add 5 to both sides of the equation Add 3 to both sides of the equation
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Ответ:
Add 3 to both sides of the equation
Solution:
The first step is to basically realize that all it's asking you to do is to find a way to make the expression on the left (
) into an expression that is a perfect square. So what number should you add to both sides such that
can be factored into
? Well, we can approach it like this:
Since
can be turned into
, and our original form was
, we quickly realize that
. From there, we can easily tell that ![p = 4](/tpl/images/1341/1674/d086d.png)
Plug this into our last value
to get 16. Therefore, if we compare this with our original equation again
, we notice that 13 + j = 16.
Thus, j = 3 for the last answer.
Add 3 to both sides of the equation.
Note: With more practice, you will quickly gain enough intuition to notice that
is very close to
which can be factored into
. But for now, the solution above will suffice. I hope this helps :))
Ответ: