How do you solve w ^ { 2} - 6w + 9= 13?

2 Answers
Nov 3, 2016

w = 3+-sqrt(13)

Explanation:

Given:

w^2-6w+9 = 13

Note that the left hand side is already a perfect square trinomial, so we have:

(w-3)^2 = 13

Taking the square root of both sides, allowing for both possible square roots, we have:

w-3 = +-sqrt(13)

Then add 3 to both sides to get:

w = 3+-sqrt(13)

Nov 3, 2016

w=3+-sqrt13

Explanation:

w^2-6w+9=13
Rearrange
w^2-6w-4=0
Either use the formula w=(-b+-sqrt(b^2-4ac))/(2a)
Where aw^2+bw+c=0
w=(6+-sqrt(36-4*1*-4))/2
w=(6+sqrt(36+16))/2 or w=(6-sqrt(36+16))/2
w=(6+sqrt52)/2=3+sqrt13
Or
w=3-sqrt13

The other way is completing the square ( which is how the formula is derived)
w^2-6w-4=0
(w-3)^2=w^2-6w+9
So w^2-6w-4 can be written (w-3)^2-13=0
(w-3)^2=13
Take the square root of both side
w-3=+-13
w=3+-13