solve by completing the square method-

1.6m²+m=2

2.4p²+7=12p

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solve by completing the square method-
1 6m2 +m=2
2 4p2 +7=12p

Harleen Birdi · Accepted Answer

Dear Student!! (1) 6m2 + m = 2 dividing throughout by 6 $m^{2} + \frac{m}{6} = \frac{1}{3} \Rightarrow m^{2} + \frac{m}{6} + (\frac{1}{12})^{2} - (\frac{1}{12})^{2} = \frac{1}{3} [adding and subtracting (\frac{1}{12})^{2}] \Rightarrow {m^{2} + 2 m (\frac{1}{12}) + (\frac{1}{12})^{2}} = \frac{1}{3} + (\frac{1}{12})^{2} \Rightarrow {(m+ \frac{1}{12})}^{2} = \frac{1}{3} + \frac{1}{144} \Rightarrow {(m+ \frac{1}{12})}^{2} = \frac{49}{144} \Rightarrow (m+ \frac{1}{12}) = \sqrt{\frac{49}{144}} \Rightarrow (m+ \frac{1}{12}) = \pm \frac{7}{12} \Rightarrow m= \pm \frac{7}{12} - \frac{1}{12} \Rightarrow m= \frac{7}{12} - \frac{1}{12} or m= \frac{- 7}{12} - \frac{1}{12} \Rightarrow m= \frac{1}{2}, \frac{- 2}{3}$ Hence, roots of the equation are $\frac{1}{2}, \frac{- 2}{3}$ (2) 4p2 + 7 = 12p â‡’ 4p2 â€“ 12p + 7 = 0 â‡’ (2p)2 â€“ 2(2p)3 + (3)2 â€“ (3)2 + 7 = 0 (adding & subtracting (3)2) â‡’ (2p â€“3)2 â€“ 9 + 7 = 0 â‡’ (2p â€“3)2 = 2 $\Rightarrow 2 p - 3 = \pm \sqrt{2} \Rightarrow 2 p = 3 \pm \sqrt{2} \Rightarrow p = \frac{3 \pm \sqrt{2}}{2}$ Thus, roots of the equation are $\frac{3 \pm \sqrt{2}}{2}$ Cheers !!

solve by completing the square method- 1.6m2 +m=2 2.4p2 +7=12p

solve by completing the square method-

1.6m²+m=2

2.4p²+7=12p