Question

Solve for x: $\sqrt{6x+7}-(2x-7)=0$

Answer 1

We have, $\sqrt{2x+9}-(2x-7)=0$

$\sqrt{2x+9}=(2x-7)$

On squaring both sides

${\left(\sqrt{6x+7}\right)}^2=(2x-7{)}^2$

$\Rightarrow 6x+7=4x^2+49-28x$

$\Rightarrow 4x^2+42-34x=0$

$\Rightarrow 2x^2-17x+21=0$

$\Rightarrow 2x^2-14x-3x+21=0$

$\Rightarrow 2x(x-7)-3(x-7)=0$

$\Rightarrow (2x-3)(x-7)=0$

$\Rightarrow x=\frac{3}{2}$ or 7

$\therefore x=7$ (as $x=3/2$ doesn't satisfy the given equation)
N.B. : always check if the original equation is satisfied by all the values you got