Question

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

Answer 1

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 :))