Solve for x if 0 ≤ x <2π.
25 cos^2 x -15 cos x - 4 = 0 (give answer to the nearest tenth)
25 cos^2 x -15 cos x - 4 = 0 (give answer to the nearest tenth)
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25 cos^2 x -15 cos x - 4 = 0
(5cosx - 4)(5cosx + 1) = 0
5cosx - 4 = 0 or 5cosx + 1 = 0
cosx = 4/5 or cosx = -1/5
x = 0.644 or x = 5.640 or x = 1.772 or x = 4.511
(5cosx - 4)(5cosx + 1) = 0
5cosx - 4 = 0 or 5cosx + 1 = 0
cosx = 4/5 or cosx = -1/5
x = 0.644 or x = 5.640 or x = 1.772 or x = 4.511
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Let cos x be u for a moment, then you're really doing
25u^2 - 15u - 4 = 0
which factors, (5u + 1)(5u - 4) = 0, and so u = -1/5 or 4/5.
So you want cos x = -1/5 or cos x = 4/5. From there, you'll need a calculator - it isn't one of the "nice" angles.
25u^2 - 15u - 4 = 0
which factors, (5u + 1)(5u - 4) = 0, and so u = -1/5 or 4/5.
So you want cos x = -1/5 or cos x = 4/5. From there, you'll need a calculator - it isn't one of the "nice" angles.