Question

Can someone please explain completing the square? The question is:
"Toni is solving this equation by completing the square"
ax^2+bx+c=0 (where "a" is greater than or equal to 0)

Step 1: ax^2+bx=-c
Step 2: x^2+b/a x=-c/a
Step 3: ?

(I have to figure out what the third step is)

Answer 1

Here's how it is done:
To complete the square:
Move the "non X" term to the right:
ax^2+bx+c=0
ax² + bx = -c
Divide the equation by the coefficient of X² which in this case is 'a'
x² + bx/a = -c/a
Now for "completing the square" we:
take the coefficient of x which is b/a
divide that by 2
b/2a
square that number
b²/4a²
then add it to both sides of the equation
x² + bx/a +b²/4a² = -c/a +b²/4a²
Take the square root of BOTH sides of the equation

Answer 2

It's a lot easier to see when using real numbers:
x² + 12x - 8=0
x² + 12x = 8
take the coefficient of X which is 12 divide it by 2 then square that number:
12/2 = 6 and
6² = 36
add 36 to both sides of the equation
x² + 12x +36 = 8 +36
Take the square root of BOTH sides of the equation
(x+6) = sqrt(44)
x = sqrt(44) -6
x = 0.6332496
x = -12.6332496

Yes, it's just that simple.
LOL

Answer 3

Thanks! I appreciate it!