x^2+6x=7 upload (6/2)^2=9 to each and each part. x^2+6x +9=7 +9 This completes the sq. on the left on account that by employing factoring you get (x+3)^2 = 16 From the following you are able to take the sq. root x+3= +/- 4 x=3 +/- 4 = -7 and a million
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Note that, by the cosine double-angle formula:
cos(2x) = 2cos^2(x) - 1.
Replacing x with x/2 gives:
cos(x) = 2cos^2(x/2) - 1.
So, we have:
cos(x/2) = 1 + cos(x) = 2cos^2(x/2)
==> 2cos^2(x/2) - cos(x/2) = 0, by setting the right side equal to 0
==> cos(x/2)[2cos(x/2) - 1] = 0, by factoring out cos(x/2)
==> cos(x/2) = 0 and cos(x/2) = 1/2, by the zero-product property.
From the unit circle:
(a) cos(x/2) = 0:
x/2 = π/2 ± πk ==> x = π ± 2πk
(b) cos(x/2) = 1/2:
x/2 = π/3 ± 2πk and x/2 = 5π/3 ± 2πk ==> x = 2π/3 ± 4πk and x = 10π/3 ± 4πk.
On the required interval, x = 2π/3 and x = π.
I hope this helps!
x^2+6x=7 upload (6/2)^2=9 to each and each part. x^2+6x +9=7 +9 This completes the sq. on the left on account that by employing factoring you get (x+3)^2 = 16 From the following you are able to take the sq. root x+3= +/- 4 x=3 +/- 4 = -7 and a million