MHB Help with Quadratic Equations by completing the square

[Maddsnicole]

I understand how to solve these equations when the square is on this side of the equal sign: x² + 8x + 7 = 27

But when the square is on the other side, I am thrown. Like this one...
x² = 14x - 33

The solutions manual shows the next step as the following, but what do you do to get to this point?
x² - 14x + 49 = -33 + 49

 

[MarkFL]

We are given:

$$x^2=14x-33$$

Subtract through by $14x$:

$$x^2-14x=-33$$

Take the coefficient of the linear term which is -14, divide by 2 to get -7, then square to get 49, and so add 49 to both sides:

$$x^2-14x+49=-33+49$$

Does this make sense?

 

[hedgehog380]

I understand how to solve these equations when the square is on this side of the equal sign: x² + 8x + 7 = 27

But when the square is on the other side, I am thrown. Like this one...
x² = 14x - 33

The solutions manual shows the next step as the following, but what do you do to get to this point?
x² - 14x + 49 = -33 + 49

I would not have followed the solution manuals next step. From the question

x² = 14x - 33

I would first move everything over to the left hand side (because this is where the x² is).

When you do this the terms you move from one side to the other need to change signs (positive becomes negative, negative becomes positive) so you should get this:

x² - 14x + 33 = 0

From here I would complete the square as normal.