Question

how to factorize a^2 - a - 10 = 0

Answer 1

$\small \bf \pink{hey \: mate \: here \: is \: ur \: ans} \\ \\ \small \bf \pink{ \huge \: solution} \\ \\ \small \bf \pink{ {a}^{2} - a - 10 = 0} \\ \\ \small \bf \pink{ \underline{ \underline{step \: by \: step \: explaination}}} \\ \\ \small \bf \pink{method = completing \: square \: method} \\ \\ \small \bf \pink{( {a)}^{2} - 2 \times a \times \frac{1}{2} + { (\frac{1}{2} )}^{2} - {( \frac{1}{2}) }^{2} - 10 = 0} \\ \\ \small \bf \pink{(a - \frac{1}{2} )^{2} - \frac{1}{4} - 10 = 0} \\ \\ \small \bf \pink{(a - \frac{1}{2} )^{2} - \frac{ 1 - 40}{4} = 0} \\ \\ \small \bf \pink{(a - \frac{1}{2} )^{2} - \frac{41}{4} = 0} \\ \\ \small \bf \pink{(a - \frac{1}{2} ) ^{2} = \frac{41}{4} } \\ \\ \small \bf \pink{a - \frac{1}{2} = \pm \sqrt{ \frac{41}{4} } } \\ \\ \small \bf \pink{a = \frac{ \sqrt{41} }{2} + \frac{1}{2} } \\ \\ \small \bf \pink{a = \frac{1 + \sqrt{41} }{2} } \\ \\ \small \bf \pink{and \: } \\ \\ \small \bf \pink{a = \frac{1 - \sqrt{41} }{2} \: \: \: ans}$