Question

6. Solve for x
$2 {x}^{2} + 6 \sqrt{3} x - 60 = 0$
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Answer 1

Answer:

${2x}^{2} + 6 \sqrt{3} x - 60 = 0$

${x}^{2} + 3 \sqrt{3} x - 30 = 0$

${ x}^{2} + 5 \sqrt{3} x - 2 \sqrt{3 } x - 30 = 0$

$x(x + 5 \sqrt{3} ) - 2 \sqrt{3} (x + 5 \sqrt{3} )$

$(x + 5 \sqrt{3} )(x - 2 \sqrt{3} )$

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Answer 2

$Given \: 2x^{2} + 6\sqrt{3}x - 60 = 0$

/* Divide each term by 2 , we get */

$\implies x^{2} + 3\sqrt{3}x - 30 = 0$

/* Splitting the middle term, we get

$\implies x^{2} + 5\sqrt{3}x - 2\sqrt{3}x - 30 = 0$

$\implies x( x + 5\sqrt{3} ) - 2\sqrt{3} ( x + 5\sqrt{3})$

$\implies ( x + 5\sqrt{3} )(x - 2\sqrt{3}) = 0$

$\implies x + 5\sqrt{3} = 0 \: Or \: x - 2\sqrt{3} = 0$

$\implies x = - 5\sqrt{3} = 0 \: Or \: x = 2\sqrt{3}$

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