x^2-12x=4 What number needs to be added to complete the square.

Question

dangerousjesse · Answer

What was your first impression of this problem? Any guesses?

oreolover4876 · Answer

I honestly have no clue, this is from a section i havent learned yet and my teacher said that a problem like it is going to be on my final

dangerousjesse · Answer

Okay, I hope you don't mind me taking a minute to explain this haha.

dangerousjesse · Answer

Complete the square:
$$x^{2}-12 x = 4$$

Subtract 4 from both sides:
$$x^{2}-12 x-4 = 0$$

Add 4 to both sides:
x^2-12 x = 4

Group terms together on the left hand side, leaving a blank spot to add a constant in later:
$$(x^2-12 x+    ) = 4$$

Take one half of the coefficient of x and square it, then add it to both sides.
Add $$\frac{-12}{2}^{2} = 36$$ to both sides:
$$(x^{2}-12 x+36) = 4+36$$

$$4+36 = 40:$$
$$(x^2-12 x+36) = 40$$

$$x^2-12 x+36 = (x-6)^2:$$

oreolover4876 · Answer

Thank you sooo much!!

dangerousjesse · Answer

$$(x-6)^{2}-40=0$$

dangerousjesse · Answer

No problem :)