Question

question
what is the intermediate step in the form (x + a)^2 = b as a result of completing the square for the following equation?

x^2 - 16x + 13 = -10x

answer attempt 1 out of 2

(□)^2 = □

Explanation:

Step1: Rearrange the equation

First, move all terms involving \(x\) to one - side.
\(x^{2}-16x + 10x+13 = 0\), which simplifies to \(x^{2}-6x+13 = 0\). Then, \(x^{2}-6x=-13\).

Step2: Complete the square

For the left - hand side \(x^{2}-6x\), take half of the coefficient of \(x\), square it and add it to both sides. The coefficient of \(x\) is \(-6\), half of it is \(- 3\), and its square is \(9\).
\(x^{2}-6x + 9=-13 + 9\).

Step3: Rewrite in the desired form

The left - hand side can be written as a perfect square \((x - 3)^{2}\), and the right - hand side is \(-4\). So, \((x - 3)^{2}=-4\).

Answer:

\((x - 3)^{2}=-4\)