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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

User Amjith
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1 Answer

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Answer:

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 (
x^2 - 8x + 13) into an expression that is a perfect square. So what number should you add to both sides such that
x^2 - 8x + (13 + j) can be factored into
(x-p)^2 ? Well, we can approach it like this:

Since
(x-p)^2 can be turned into
x^2 -2px + p^2, and our original form was
x^2 - 8x + (13 + j), we quickly realize that
-2px = -8x. From there, we can easily tell that
p = 4

Plug this into our last value
p^2 to get 16. Therefore, if we compare this with our original equation again
x^2 - 8x + (13 + j), 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
x^2 - 8x + 13 is very close to
x^2 - 8x + 16 which can be factored into
(x-4)^2. But for now, the solution above will suffice. I hope this helps :))

User Amir Pashazadeh
by
8.6k points

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