How do you solve w2−6w+9=13?

2 Answers
George C.
Nov 3, 2016

w=3±√13

Explanation:

Given:

w2−6w+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=±√13

Then add 3 to both sides to get:

w=3±√13

Annie
Nov 3, 2016

w=3±√13

Explanation:

w2−6w+9=13
Rearrange
w2−6w−4=0
Either use the formula w=−b±√b2−4ac2a
Where aw2+bw+c=0
w=6±√36−4⋅1⋅−42
w=6+√36+162 or w=6−√36+162
w=6+√522=3+√13
Or
w=3−√13

The other way is completing the square ( which is how the formula is derived)
w2−6w−4=0
(w−3)2=w2−6w+9
So w2−6w−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

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