Solve the quadratic equation by completing the square.

Question

-3x^2+9x=1

Not sure how to do these, if someone could expplain.

Answer 1

it's usually easier to have a positive coefficient for x^2, so let's take care of that first:

3x^2 - 9x = -1
x^2 - 3x = -1/3

since (x-a)^2 = x^2 - 2a + a^2, you want to take half of 3 and square it, then add that to both sides:

x^2 - 3x + 9/4 = -1/3 + 9/4

Now you have a perfect square on the left:

(x-3/2)^2 = 23/12

now take square roots:

x - 3/2 = ±√(23/12) = ±√69/6

so,

x = 3/2 ±√69/6
or,
x = (9±√69)/6

Note how that is the solution using the quadratic formula.

Answer 2

Still confused, but I'll try another one and see if I get it. Thank you.