Solve (w+1)^2-50=0, Where is a real number. Simplify your answer as much as possible.
w=
Answer:
(w+1)^2-50=0
square the terms in the parenthesis. Dont forget the middle term!
w^2 +2w +1 -50 = 0
combine like terms
w^2 + 2w - 49 = 0
it is a quadratic function, there are multiple ways to solve it
(-2 (+/-) sqrrt(2^2 -(4)(1)(-49)) )/ 2(1)
(-2 (+/-) sqrrt(200) )/2
now since 200 isnt a perfect root we should try to pull squares out of it. 25*8 =200
(-2 (±) 5(sqrrt(8))) /2
4*2 = 8
(-2 (+/-) 10(sqrrt(2)) /2
***** this also could have been found with 100*2 = 200 and pulling the root of 100 out. if you ever don’t simplify it all the way in the first go you can continue working it ********
We can now divide both leading terms by two and get rid of the fraction
-1 (+/-) 5(sqrrt(2))
x = -1 + (5)(sqrrt(2) = about 6.07
x = -1 - (5)(sqrrt(2) = about -8.07
you can also complete the square
w^2 + 2w - 49 = 0
w^2 + 2w = 49
(w + 1)^2 = 50
then take the root of both sides and solve for x
w+1 = (+/-) sqrt(50)
w = -1 (+/-) sqrt(50)
which simplifies to
w = -1 (+/-) 5(sqrrt(2))
this yields the same answers so both of these answers are simplified as much as they can be
