Question

solve for x by factorisation :
$3 \sqrt{5} x {}^{2} + 25x + 10 \sqrt{5} = 0$
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Answer 1

Solve by factorisation.

$3 \sqrt{5} {x}^{2} + 25x + 10 \sqrt{5}$

Solution.

$3 \sqrt{5} {x}^{2} + 25x + 10 \sqrt{5} \\ \\ = > 3 \sqrt{5} {x}^{2} + 30x - 5x + 10 \sqrt{5} \\ \\ = > 3 \sqrt{5} x(x + 2 \sqrt{5} ) - 5(x + 2 \sqrt{5} ) \\ \\ = > (3 \sqrt{5} x - 5) \: \: \: (x + 2 \sqrt{5} ) \\ \\ = > 3 \sqrt{5} x - 5 = 0 \: \: \: \: \: \: x + 2 \sqrt{5} = 0 \\ \\ = > 3 \sqrt{5}x = 5 \: \: \: \: \: \: \: \: \: x = - 2 \sqrt{5} \\ \\ \boxed{ = > x = \frac{5}{3 \sqrt{5} } \: \: \: \: \: \: \: \: \: \: \: x = - 2 \sqrt{5} }$

Rules to solve factorisation.

(1) First multiply 1st term with last term

i.e 3√5x² * 10√5 = 150x²

(2) Split middle term in that way so that after multiple the numbers answer would be 150x² and after adding/ sub it answer would be 25x

(3) Then find common between first'two terms and other two terms .

(4) After this refer above to solve factorisation ...

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