Question

Example 8 : Find the roots of the equation 3
the square.
the method of completing
ie
a the roots of the equation 5x^2- 6x -2=0 by completing square method​

Answer 1

$\huge \bf{Answer} \\ X= -0.16 \:\:or\:\: 1.36 \\ \\ \\ \huge\red{ \bf{Solution}} \\ \\ \red{ solved \: by \: square \: completing \: method} \\ \\5 {x}^{2} - 6x - 2 = 0 \\ \\ \star \: \underline{ step \: 1 } \pink{\implies \: \: \: divide \: all \: term\: by \: co - efficient} \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: of \: {x}^{2} \\ \\ we \: get, \: \\ {x}^{2} - 1.2x + 0.4 = 0 \\ \\ \star \: \underline{step \: 2} \implies \: \: \green{move \: constant \: term \: to \: right \: side }\\ \\ we \: get ,\\ {x}^{2} - 1.2x = 0.4 \: \\ \\ \star \: \underline{ step \: 3} \implies \red{ complete \: the \: square. }\\ \\ {x}^{2} + {(0.6)}^{2} - 1.2x = 0.4 + 0.36 \\ \\ \implies \: {(x - 0.6)}^{2} = 0.76 \\ \\ \therefore \\ \: if \: + 0.76 \\ \implies \: x - 0.6 = + 0.76 \\ \\ \implies \: \boxed{ x = 1.36 }\\ \\ if \: - 0.76 \\ \\ \implies \: x - 0.6 = - 0.76 \\ \\ \implies \: \boxed{x = - 0.16}$