<prompt> Pata thamani zote za x zinazokidhisin 4 arctan x frac2425.Ingiza suluhu zote, zikitenganishwa na koma.  <response>: Acha theta arctan x. Kisha kutoka kwa fomula ya pembe mbili,anzaaligndhambi 4 theta 2 dhambi 2 theta cos 2 theta 4 sin theta cos theta 2 cos2 theta - 1.endalignKwa kuwa theta arctan x, x tan theta. Kisha cos theta frac1sqrtx2 1 na sin theta fracxsqrtx2 1, hivyoanzaaligndhambi 4 theta 2 dhambi theta cos theta 2 cos2 theta - 1 4 cdot fracxsqrtx2 1 cdot frac1sqrtx2 1 cdot left 2 cdot frac 1x2 1 - 1 kulia -frac4x x2 - 1x2 12 frac2425.endalignHii hurahisisha6x4 25x3 12x2 - 25x 6 0.Hii huzingatia kama x 2x 32x - 13x - 1 0, kwa hivyo suluhu ni -3, -2, frac13, frac12. 