Question

SOLVE FOR X
$\sqrt{6x + 7 \: \: } - (2x - 7) = 0$

Answer 1

The answer is given below :

Now,

$\sqrt{6x + 7 \: \: } - (2x - 7) = 0 \\ \\ or \: \: \sqrt{6x + 7 \: \: } = (2x - 7) \\ \\ now \: \: squaring \: \: we \: \: get \\ \\ 6x + 7 = {(2x - 7)}^{2} \\ \\ or \: \: 6x + 7 = 4 {x}^{2} - 28x + 49 \\ \\ or \: \: 4 {x}^{2} - 34x + 42 = 0 \\ \\ or \: \: 2 {x}^{2} - 17x + 21 = 0 \\ \\ or \: \: 2 {x}^{2} - 14x - 3x + 21 = 0 \\ \\ or \: \: 2x(x - 7) - 3(x - 7) = 0 \\ \\ or \: \: (x - 7)(2x - 3) = 0 \\ \\ either \: \: x - 7 = 0 \: \: or \: \: 2x - 3 = 0 \\ \\ therefore \: \: the \: \: required \: \: \\ soution \: \: is \\ \\ x = 7 \: \: and \: \: x = \frac{3}{2}$

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