Answer:
[tex]-k^2[/tex] and [tex]-12k[/tex] is added to both sides because we want to have all the terms with [tex]k[/tex] on the left side of the equation. [tex]-\frac{1}{16}[/tex] is multiplied because it is just the same as dividing by [tex]-16[/tex].
Step-by-step explanation:
Starting from [tex]k^{2} -4k+13=k^2+12k+37[/tex]:
In any equation, we can remove equal terms on both sides. We can apply this to the equation above. In the equation above, the equal terms are [tex]k^2\\[/tex]. We can remove [tex]k^{2}[/tex] by adding [tex]-k^2[/tex] to both sides (left and right sides).
The equation is now: [tex]k^2-k^2-4k+13=k^2-k^2+12k+37[/tex]. Since [tex]k^2-k^2 = 0[/tex], the equation becomes [tex]-4k+13=12k+37[/tex].
Then, to solve for [tex]k[/tex], we can move all the terms that has [tex]k[/tex] to the left side, and move everything else to the right side. In [tex]-4k+13=12k+37[/tex] , we can see that [tex]-4k[/tex] is already at the left side, and we only need to move [tex]12k[/tex] to the left side. We do this by moving [tex]12k[/tex] from the right side to the left side, but we have to change the sign from + (positive) to - (negative). This is a rule whenever we move terms to different sides. Moving [tex]12k[/tex] is the same as adding [tex]-12k[/tex] to both sides. When we do this, we get:
[tex]-4k-12k+13=12k-12k+37[/tex]
[tex]-16k+13=37[/tex]
Then we move the constant [tex]13[/tex] to the right side, by moving [tex]13[/tex] and changing the sign so that it becomes [tex]-13[/tex]. This is the same as The equation becomes [tex]-16k=24[/tex].
To solve for [tex]k[/tex], we need to divide both sides by [tex]-16[/tex]. This is because [tex]-16[/tex] is multiplied to [tex]k[/tex], and to remove [tex]-16[/tex], we do the opposite of multiplication: division.
Remember that dividing something by a number is the same as multiplying that something by 1 over the number. This is why the explanation says: multiply[tex]-\frac{1}{16}[/tex] to both sides, which is the same as dividing by [tex]-16[/tex].
