\((4x-2)^2+6x=25\) āĻĻā§āĻŦāĻŋāĻāĻžāĻ¤ āĻ¸āĻŽā§āĻāĻ°āĻ¨ā§āĻ° āĻŦāĻžāĻ¸ā§āĻ¤āĻŦ āĻŦā§āĻ āĻĨāĻžāĻāĻ˛ā§ āĻļā§āĻ°ā§āĻ§āĻ° āĻāĻāĻžāĻ°ā§āĻ¯ā§āĻ° āĻ¸ā§āĻ¤ā§āĻ°ā§āĻ° āĻ¸āĻžāĻšāĻžāĻ¯ā§āĻ¯ā§ āĻ¨āĻŋāĻ°ā§āĻŖā§ āĻāĻ°āĻŋ āĨ¤
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\((4x-2)^2 + 6x=25\)
āĻŦāĻž, \((4x)^2-2.4x.2+2^2+6x-25=0\)
āĻŦāĻž, \(16x^2-16x+6x+4-25=0\)
āĻŦāĻž, \(16x^2-10x-21=0\)
\(16x^2-10x-21=0\) āĻ¸āĻŽā§āĻāĻ°āĻ¨āĻāĻŋāĻā§ \(ax^2+bx+c=0\) āĻ¸āĻŽā§āĻāĻ°āĻ¨ā§āĻ° āĻ¸āĻā§āĻā§ āĻ¤ā§āĻ˛āĻ¨āĻž āĻāĻ°ā§ āĻĒāĻžāĻ
\(a=16, b=-10\) āĻāĻŦāĻ \(c=-21\)
āĻāĻāĻ¨ āĻļā§āĻ°ā§āĻ§āĻ° āĻāĻāĻžāĻ°ā§āĻ¯ā§āĻ° āĻ¸ā§āĻ¤ā§āĻ° āĻŦā§āĻ¯āĻŦāĻšāĻžāĻ° āĻāĻ°ā§ āĻĒāĻžāĻ,
\(x=\cfrac{-(-10)\pm\sqrt{(-10)^2-4\times 16\times (-21)}}{2\times 16}\)
\(=\cfrac{10\pm\sqrt{100+1344}}{32}\)
\(=\cfrac{10\pm\sqrt{1444}}{32}\)
\(=\cfrac{10\pm 38}{32}\)
āĻšā§, \(x=\cfrac{10+38}{32}=\cfrac{48}{32}=\cfrac{3}{2}\)
āĻ¨ā§, \(x=\cfrac{10-38}{32}=-\cfrac{28}{32}=-\cfrac{7}{8}\)
\(\therefore \) āĻ¨āĻŋāĻ°ā§āĻŖā§ā§ āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ \(x=\cfrac{3}{2}, -\cfrac{7}{8}\)