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

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

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 :))

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