Verified answer

w = (6 - w)^2

w = 36 - 12w + w^2

hence w^2 - 13w + 36 = 0

=> (w - 4) (w - 9) = 0

so w = 4 OR w = 9 <<<<<<<<<<<<<,

NOTE : check these 2 answers in the eqn and u will find out that they both are correct .

u did an error by writing w = w^2-13w+36 , it should be : 0 = w^2-13w+36

You see the w^2, so that tells you it's a quadratic equation. Put it in standard form, meaning put everything on the same side.

w^2 - 13w + 36 - w = 0

w^2 - 14w + 36 = 0

Now solve it with standard methods. It doesn't factor, so plug it into the quadratic formula instead. a = 1, b = -14, c = 36.

Edit: Actually (6 - w)^2 = w^2 -12w + 36, and when you put it in standard form you have

w^2 - 13w + 36 = 0 which DOES factor.

you have 0 on left side after subtracting w from both sides then factor

0 = w^2 - 13w + 36

0 = (w - 9)(w - 4)

w = 9 or w = 4

√w = 6-w.............you squared both sides.............VERY GOOD

w=(6-w)(6-w)..........CORRECT.........now you F.O.I.L.ed

w=w^2-13w+36...............should be ......-12w

w=w^2-12w+36

-w........-w

0=w^2-13w+36

w^2-13w+36=0

w^2-13w+__=-36+__............when coefficient of w is ODD (or coefficient of w^2 is NOT one, I do the following

Here is a method 99% of teachers do not know

Last book it was in was about 1898

The "beauty" of this method is you DON'T have to work with FRACTIONS until the end of the problem

The book "trick' is to take 1/2 of b (coefficient of x), then square it and that is what you add to both sides

TRY THIS

The "old trick" was to MUTIPLY EACH TERM BY 4a (4 times the coefficient of x^2) and to ADD b^2 to both sides.

Let's try it..................

2x^2-6=x..................switch sides with the "-6" and the "+x"

2x^2-x=+6

a=2......b=-1................coefficients of a and b

4a = 4(2)= 8.................MULTIPLY every term by 8

16x^2-8x=48

b^2=(-1)^2=+1.................This is what you ADD to both sides

16x^2-8x+1=48+1..........You now have a Perfect Square Trinomial on the left side which is the "purpose"

........................................of Completeing the Square.........this factors into a binomial squared

..................................(square root of first term.....same sign as the middle term......square root of last)^2

(4x-1)^2=49...............Take the square root of both sides (dont forget the +- sign on the right side)

sqrt[(4x-1)^2]=+-sqrt[49]

4x-1=+-7

4x-1=+7...............4x-1=-7...............Add 1 to both sides of both equations

4x=8...............4x=-6

x=2.............x=-6/4=-3/2...........our first fraction......but who cares..........we are finished

LIKE I SAID EARLIER MOST TEACHERS/STUDENTS DO NOT KNOW THIS METHOD

TEACH THEM................They will love you

Multiply by 4a = 4(1)=4

Add b^2 =(-13)^2=169

4w^2-52w+169=-36+169

(2w-13)^2=133

sqrt(2w-13)^2=+-sqrt(133)

2w-13=+-sqrt(133)

2w=+13+-sqrt(133)

w=[+13+-sqrt(133)]/2............ANSWSER