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4cos4x+4cos2x+1=0 equation

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Numerical solution:

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The solution

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4*cos(4*x) + 4*cos(2*x) + 1 = 0
$$\left(4 \cos{\left(2 x \right)} + 4 \cos{\left(4 x \right)}\right) + 1 = 0$$
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Numerical answer [src]
x1 = 5.70980266352751
x2 = -42.1994853037168
x3 = 40.2673218530152
x4 = 52.048294303977
x5 = -11.9929879707071
x6 = -31.98930917955
x7 = 8.06599715371985
x8 = 48.4826706108964
x9 = -52.048294303977
x10 = -53.9804577546786
x11 = 11.9929879707071
x12 = 86.1817824539739
x13 = 74.0394428791055
x14 = -16.281345911601
x15 = 81.1080263496825
x16 = -3.71497529724187
x17 = -20.2083367285883
x18 = -75.9716063298071
x19 = 99.9575822712213
x20 = -82.2547916369867
x21 = -77.9664336960927
x22 = -45.7651089967974
x23 = -57.9074485716658
x24 = 9.99816060442146
x25 = 26.9155530752586
x26 = 66.5468283690377
x27 = 70.473819186025
x28 = -86.6058134934647
x29 = -13.9251514214087
x30 = -86.1817824539739
x31 = 42.1994853037168
x32 = -74.0394428791055
x33 = 84.2496190032723
x34 = 39.057892650127
x35 = 93.6743969640417
x36 = -64.6146649183361
x37 = -1.78281184654027
x38 = 18.2761732778867
x39 = -60.2636430618581
x40 = -89.7474061470545
x41 = 92.4649677611535
x42 = -64.1906338788454
x43 = -99.9575822712213
x44 = -33.9841365458356
x45 = -5.70980266352751
x46 = -9.99816060442146
x47 = -69.6884210226275
x48 = -30.0571457288484
x49 = -93.6743969640417
x50 = 87.3912116568621
x51 = 13.9251514214087
x52 = -27.7009512386561
x53 = 62.2584704281438
x54 = 0.573382643652078
x55 = 1.78281184654027
x56 = 75.9716063298071
x57 = 45.3410779573066
x58 = -38.2724944867296
x59 = 16.281345911601
x60 = 4.92440450013006
x61 = -49.6920998137846
x62 = -96.0305914542341
x63 = -14078.8354615429
x64 = 82.2547916369867
x65 = 60.2636430618581
x66 = 89.3233751075637
x67 = -79.8985971467944
x68 = -71.6832483889132
x69 = 71.6832483889132
x70 = 88.5379769441663
x71 = 77.9664336960927
x72 = -67.7562575719259
x73 = 67.3322265324352
x74 = -35.9162999965373
x75 = 96.0305914542341
x76 = 27.7009512386561
x77 = 20.2083367285883
x78 = -97.9627549049357
x79 = -47.697272447499
x80 = -23.3499293821781
x81 = 38.2724944867296
x82 = 33.9841365458356
x83 = -55.9752851209642
x84 = 44.5556797939092
x85 = 31.98930917955
x86 = 30.0571457288484
x87 = -8.06599715371985
x88 = 49.6920998137846
x89 = -23.7739604216688
x90 = 97.9627549049357
x91 = 22.5645312187806
x92 = 53.9804577546786
x93 = -91.6795695977561
x94 = 23.7739604216688
x95 = 64.1906338788454
x96 = 55.9752851209642
x97 = -25.7061238723704
x97 = -25.7061238723704