so
ok so
any quadratic equation can be put into the form
y=ax²+bx+c
where a,b, and c are constants
a is the leading coefient
b is the linear coefient
c is the constant
to solve, we have it equal to 0
easly do that exmple, if we had
3=2x²-4x+2, minus 3 from both sides to get
0=2x-4x-1, get it equal to 0
so
here are the steps to complete the square
1. make sure that one side is equal to 0 by subtracting whatever is on one side
2. group the x terms together with parenthaees
3. undistribute the leading coefient from inside the parenthasees
4. take 1/2 of the linear coefiet and square it, add negative and positive of it inside the parenthasees
5. factor perfect square trinomial
6. distribute and add like terms
7. subtract the constant from both sides
8. divide both sides by the leading coefient you factored out
9. square root both sides and remember to get the positive and negative root of the constant side
10. solve for x
so, a demonstration
3=4x²-8x+2
first, equal to 0
minus 3 both sides
0=4x²-8x-1
next, group x terms together with parenthaees
0=(4x²-8x)-1
factor out linear coefient
0=4(x²-2x)-1
take 1/2 of linear coefient and square it, then take positive and negative and add to inside
-2/2=-1, (-1)²=1,
0=4(x-2x+1-1)-1
factor perfect square trinomial
0=4((x-1)²-1)-1
distibute and add like terms
0=4(x-1)²-5
add the constant to both sides
5=4(x-1)²
divide oth sides by the factored out leading coefient
5/4=(x-1)²
sqrt both sides, remember to take positive and negaite roots
+/-(√5)/2=x-1
solve for x
add 1 to both sides
1+/-(√5)/2=x
(2+/-√5)/2=x
x=(2+√5)/2 or x=(2-√5)/2
that is how you use the coomplete square to solve